| Coulomb's Law
Electric Potential and Capacitance Electric Current, Resistance, and Circuits Magnetism Magnetic Induction AC Circuits |
Geometric Optics
Physical Optics Relativity Modern Physics |
2. A 3mC charge of mass 0.050 kg floats motionless above a 60nC charge. There are no strings attached to the charge on top. At what height is it floating if there are no other relevant forces around?
4. Two positive 3microC charges sit as shown in Fig. J:
one on the y-axis at y=3cm, the other on the negative x-axis at x=-2cm.
a) Sketch the lines of electric force in the vicinity
of the two charges. Use at least four lines coming out of (or going in
to) each charge.
b) Calculate the magnitude of the electric field at the
origin.
5. A 10-4kg, 3microC charge is suspended from
a 10cm string in a region where the E-field has a magnitude of 250N/C and
points horizontally. At what angle will the charge hang in equilibrium?
B. Sketch the electric field lines around a +2nC charge and a -1nC charge.
6. Consider a +9nC charge and a -6nC charge, 3mm to its right.
a) What is the magnitude and direction of the electric field halfway between the two charges?
b) What is the magnitude and direction of the electric field halfway between the two charges if the -6nC is replaced by +6nC?
c) What is the magnitude and direction of the force would a -1nC charge experience halfway between the two charges of part b?
7. An electron, Q=-1.6´
10-19C, is positioned at x=-2cm on the x axis. A proton sits at x=-2cm, y=-2cm. What is the magnitude and direction of the electric field at the origin?
8. Find the magnitude of the electric field at the origin, given its proximity to the following source charges:
Q1=+5nC, at x=10cm on the y-axis
Q2=-2nC, at x=6cm on the x-axis.
Indicate on a sketch the direction of the electric field.
9. A 10g mass, with a -3nC charge on it, hangs at an angle of 10° from the vertical, because of the presence of a uniform horizontal electric field. Let's say that it hangs toward the right hand side of the page.
a) What is the magnitude of the electric field?
b) What is the direction of the field?
10. You are setting up a classroom demonstration of electric forces and you have a 5 microgram pithball attached to a nearly massless string. You know that you can easily generate a horizontal 100V/m electric field near the pith ball. How much charge must you put on the ball to get it to hang at a 75o angle, measured relative to the horizontal?
11. A +3mC charge sits at the origin, a -2mC charge sits on the x-axis at x=2cm. Calculate the magnitude and direction of the electric field 2cm above the negative charge.
12. Sketch the electric field lines for four equal positive charges at the four corners of a square.
13. Calculate the magnitude and direction of the force on charge C, if charge A (-6mC) is located at the origin, charge B (+1.5mC) is located at x=3cm, and charge C (-2mC) is located at x=5cm.
14. One +2mC charge sits on the x-axis at x=-3cm, and a -3mC charge sits on the y-axis at y= +2 cm.
a) What is the magnitude and direction of the electric field at the origin?
b) What is the magnitude and direction of the force a -5nC charge sitting at the origin would feel?
16. An electric dipole lies in an electromagnetic field,
and the dipole moment points perpendicular to the field. Which one
of the following is FALSE?
a) _____ The dipole will continue to point in that direction
if no other forces act on it.
b) _____ The net force on the dipole is zero.
c) _____ The electrostatic potential energy of the dipole
is zero.
d) _____ The net charge of the dipole is zero.
17. A water molecule, which has a dipole moment of 6.2×10-30Cm,
is in a 150V/m electric field inside a microwave oven.
a) How much energy is needed to completely flip
the dipole?
b) If the oven consumes 1kW of power, what is the
maximum number of dipole flips that can occur per second?
18. An electric dipole consists of two 1microC charges
on the y-axis. The positive charge is at y=+0.5mm, the negative charge
is at y=-0.5mm.
a) Calculate the electric field at x=10mm, y=0.
b) This dipole sits in a uniform external electric field.
What must Ey be in order for the potential energy of the dipole
to be 1014eV?
19. An electric dipole consists of two charges of magnitude lnC, each located lcm away from the origin on the y-axis. The positive charge is at y=+lcm.
a) What is the dipole moment of this dipole?
b) What is the magnitude and direction of the electric field at y= lrn?
ELECTRIC POTENTIAL AND CAPACITANCE
2. Consider two charges --- a +6mC charge at x=6m, y=0,
and a -3mC charge at y=3m, x=0 ---- which act on a -2nC charge at
the origin,
a) Calculate the magnitude and direction of the
force on the -2nC charge.
b) Calculate the magnitude and direction of the
electric field on the same charge.
c) Calculate the electric potential on the -2nC
charge.
3. Which two of the following four quantities would be
zero halfway between two +1nC charges?
a) the E-field
b) the force on a test charge at that point
c) the electric potential
d) the potential energy of a test charge at that
point
4. Four charges of equal magnitude (2 positive, 2 negative)
are arranged in a square, with the postive charges at the top left and
bottom right.
a) Sketch the lines of electric force in the vicinity
of the square. Use at least four lines coming out of (or going in
to) each charge.
b) Calculate the potential at the point midway
between the top two charges. The charges each have magnitude 6mC, and are
each 2mm away from the nearest neighbors.
5. We had a formula for each of the following expressions
except one. Which one? What units would it have?
a) _____ kQ/r3
b) _____ kQ/r2
c) _____ kQq/r2
d) _____ kQ/r
6. Which of the following is FALSE?
a) _____ Electric potential is the electrical potential
energy per charge.
b) _____ The electrostatic field is the electrostatic
force per charge.
c) _____ Positive charges released from rest will move
from higher to lower potential.
d) _____ An electron will always travel from the lower
to higher electric potential.
e) _____The electrostatic force on a charge always points
in the direction of the E-field.
7. For the charge distribution below, with +5mC located
at (x,y)=(-1m,0) and -6mC located at (0,2m),
a) Calculate the magnitude and direction of the electric
field at the origin.
b) Using the results of part (a), calculate the force
that would act on a 2mC charge at the origin.
c) Calculate the electric potential at the origin.
d) How much energy would it take to move a 2mC
charge from infinitely far away (V=0) to the origin?
8. Show that the two units of electric field ( V/m and N/C ) are equivalent.
9. A +6microC charge lies on the x-axis at x=+3mm, and
a -6mC charge lies at x=-3mm.
a) Calculate the electric potential at the origin.
b) Calculate the potential at x=0.01mm. (Do not
round off till the final step!)
c) From a) and b), estimate the E-field near the
origin.
d) Calculate the E-field at x=0 directly.
10. A special constant electric-field chamber, 0.8m to
a side, has been created in which the field inside is a uniform 1000V/m,
pointing in the positive x-direction.
a) What is the potential difference between the wall
at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m,
for what point on the x-axis is the E-field zero?
11. A +3mC charge sits on the y-axis at y=+1m. A -3mC
charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+1cm.
c) and d) Calculate Ey at the origin in two
different ways.
12. Consider force, electric field, electric potential energy, and potential.
a) Name something significant that electric field and potential have in common that they don't share with either force or potential energy.
b) Name something significant that potential and potential energy have in common that they don't share with either force or electric field. (The letter 'p' does not count.)
13. A water molecule, with a dipole moment of 6.2´
10-30C×
m is sitting in a 250N/C electric field.
a) At what angle q is the potential energy of the dipole the largest? the smallest?
b) At what angle q is the magnitude of the torque acting on it the largest? the smallest?
c) How much energy is needed to flip the molecule from its lowest potential energy to its largest?
14. Find the electric potential at the origin, given the existence of the following source charges:
Q1=+2mC, at x=3m on the x-axis,
Q2=-3mC, at y=-2m on the y-axis
Sketch on your page the direction, from the origin, of increasing potential.
15. Given what we know about lines of electric force, and about equipotential lines, describe the shape of the equipotential lines far away from a +3nC and a -2nC, which are both very close together.
16. Sketch the equipotential lines around a +1pC charge and a -1pC charge.
17. A special constant-electric-field chamber, 0.8m to a side, has been created in which the field inside is a uniform l000V/m, pointing in the positive x-direction.
a) What is the potential difference between the wall at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m, for what point on the x-axis is the E-field zero?
18. A +3mC charge sits on the y-axis at y=+1m. A -3mC charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+lcm.
c) and d) Calculate Ey at the origin in two different ways.
19. A dipole consists of a +3nC charge on the y-axis at y=lmm and a -3nC charge on the y-axis at y=-lmm. a) Calculate the electric potential at x=l.000m and 1.001m.
b) Estimate the electric field from the two values in (a).
c) What is the dipole moment of this pair of charges?
20. Consider a point charge of 33nC situated at the origin.
a) Calculate the electric potential at x=1.99m and x=2.01m.
b) Use this result to estimate Ex at x=2m.
c) Calculate Ex directly.
d) What is Ey at x=2m?
21 A water molecule has a 6.2´
10-30C×
m dipole moment.
a) What is the distance between the time-averaged position of the positive and negative charges (both are single charges) which make up the dipole?
b) There is typically about a 100V/m electric field near the ground, which points vertically. How much energy does it take to flip the dipole moments for 18g of water (Avogadro's number, which equals 6.02´
1023 ) from being aligned with this field to pointing opposite the field?
22. A point charge of +33mC sits at the origin.
a) Calculate the magnitude and direction of the electric field at a point 5cm away on the positive x-axis.
b) Calculate the electric potential at x=4.999cm and at 5.001cm.
c) Use the results of part (b) to estimate Ex at x=5.000cm.
23. Consider force, electric field, electric potential energy, and potential.
a) Name something significant that electric field and potential have in common that they don't share with either force or potential energy.
b) Name something significant that potential and potential energy have in common that they don't share with either force or electric field. (The letter 'p' does not count.)
24. A water molecule, with a dipole moment of 6.2´
10-30C×
m is sitting in a 250N/C electric field.
a) At what angle q is the potential energy of the dipole the largest? the smallest?
b) At what angle qis the magnitude of the torque acting on it the largest? the smallest?
c) How much energy is needed to flip the molecule from its lowest potential energy to its largest?
25. Find the electric potential at the origin, given the existence of the following source charges:
Q1=+2mC, at x=3m on the x-axis,
Q2=-3mC, at y=-2m on the y-axis
Sketch on your page the direction, from the origin, of increasing potential.
26. Given what we know about lines of electric force, and about equipotential lines, describe the shape of the equipotential lines far away from a +3nC and a -2nC, which are both very close together.
27. Sketch the equipotential lines around a +1pC charge and a -1pC charge.
28. A special constant-electric-field chamber, 0.8m to a side, has been created in which the field inside is a uniform l000V/m, pointing in the positive x-direction.
a) What is the potential difference between the wall at x=0m and the wall at x=0.8m?
b) Which wall is at the higher potential?
c) If a +3nC charge is now added to the x-axis at x=0.4m, for what point on the x-axis is the E-field zero?
29. A +3mC charge sits on the y-axis at y=+1m. A -3mC charge sits on the y-axis at y=-1m.
a) Calculate the electric potential at the origin.
b) Calculate the electric potential at y=+lcm.
c) and d) Calculate Ey at the origin in two different ways.
30. A dipole consists of a +3nC charge on the y-axis at y=lmm and a -3nC charge on the y-axis at y=-lmm.
a) Calculate the electric potential at x=l.000m and 1.001m.
b) Estimate the electric field from the two values in (a).
c) What is the dipole moment of this pair of charges?
31. Consider a point charge of 33nC situated at the origin.
a) Calculate the electric potential at x=1.99m and x=2.01m.
b) Use this result to estimate Ex at x=2m.
c) Calculate Ex directly.
d) What is Ey at x=2m?
32. A water molecule has a 6.2´
10-30C×
m dipole moment.
a) What is the distance between the time-averaged position of the positive and negative charges (both are single charges) which make up the dipole?
b) There is typically about a 100V/m electric field near the ground, which points vertically. How much energy does it take to flip the dipole moments for 18g of water (Avogadro's number, which equals 6.02´
1023 ) from being aligned with this field to pointing opposite the field?
33. A point charge of +33mC sits at the origin.
a) Calculate the magnitude and direction of the electric field at a point 5cm away on the positive x-axis.
b) Calculate the electric potential at x=4.999cm and at 5.001cm.
c) Use the results of part (b) to estimate Ex at x=5.000cm.
35. A parallel-plate capacitor has a plate separation
of 0.08 mm (about the thickness of one sheet of paper), and a capacitance
of 47microF. If the E-field in the middle of the capacitor is 10V/m,
a) what is the voltage across the plates?
b) what is the charge on the plates?
36. Show that capacitance times the square of voltage has units of energy.
37. 110V are placed across two parallel capacitor plates.
a) Given that the dielectric strength of air is
3 MV/m, how close can you position the plates before they discharge?
b) If the capacitance is 12microF, how much charge
will the capacitor hold if there are 110V across the plates?
c) What is the electric field inside the capacitor
in part (b) if the plates are 1.5 mm apart?
38. Two pieces of aluminum foil, separated by a 0.1mm air gap, form a 3nF capacitor.
a) What is the area of the plates?
If 9V is applied across the capacitor,
b) What is the charge on the positively charged piece of foil?
c) Will the capacitor spark?
39. For purposes of calculating how much charge you need to shock someone with a spark, we can approximate your finger as being a sphere with about a 0.8cm radius.
a) What is the capacitance of your finger?
b) If you can get a spark to fly 2.5cm, how large a potential is them between your finger and the doorknob?
c) How much charge do you need on your finger to get a lcm spark?
d) If you place your open palm 2.5cm from the body of a car, and the palm has an area of 300rn2, what is the capacitance of the palm/car system?
ELECTRIC CURRENT, RESISTANCE, CIRCUITS
2. The unit of electrical current is the
a) _____ coulomb. b) _____ henry.
c) _____ ampere. d) _____ volt.
e) _____ farad.
3. A 3microF capacitor is charged by connecting it to
a 12V battery.
a) What is the final charge on the positive plate of
the capacitor?
b) If the charging circuit was designed to not exceed
10mA current at any time, what is the shortest amount of time it could
have taken to fully charge the capcitor?
c) If the capacitor sparked at the instant it became
fully charged, and if it is a parallel plate capacitor, what is the area
of the plates?
4. A cloud is 1km above the ground and holds 40C of charge.
a) If lightning is produced during a rainstorm, what
was the minimum potential difference between cloud and ground?
b) If the entire cloud discharged during a 2ms lightning
strike, what was the average current during the strike?
c) What is the resistance of the ionized air?
d) If the cloud and ground can be modeled as a parallel-plate
capacitor, what is the area of ground that the cloud covers?
5. A 12V battery delivers a very large current to your car when starting the car. If the car's circuit behaves like a 0.04W resistor,
a) How much energy is dissipated in the circuit during the half-second it takes the car to turn on?
b) How much potential energy does a single electron lose in going from one battery terminal to the other? (Give your answer in two different units of energy)
6. A 2A current running through a resistor causes it to dissipate 50W.
a) What is the resistor's resistance?
b) How many hours would it take for Avogadro's number of electrons (6.0´
1023) to flow through the resistor?
c) In order for the same resistor to dissipate twice the power, what current must run through it?
9. If we put a given voltage across a resistor, what must be done to the voltage to halve the power dissipated by the resistor?
10. A pickle, connected to 110V, puts out about 170W of
heat and light while it is glowing.
a) What is the current going through the pickle?
b) What is the resistance of the pickle?
11. A 2m length of wire of 25mm radius has a resistance of 40W.
a) What is the electric field in the wire if it carries a current of 100mA?
b) What is the resistivity of the wire?
13. A resistor rated at 1/4W is placed across the terminals
of a 9V battery.
a) What resistance will cause the resistor to dissipate
1/4 W?
b) Is the answer to (a) a minimum or a maximum
value of resistance?
c) If we string five such resistors end-to-end
in a circuit, how much current will the 9V battery allow?
d) How much power will the string of resistors
dissipate?
14. You cannot always say what the resistance of an object
is unless you specify which two points you are going to measure the resistance
across. Consider a network in which all the resistors are
100ohm, consisting of four resistors connected end-to-end in a closed loop,
with A, B, C, and D being consecutive points between resistors.
a) Calculate the resistance if you connect your resistance
meter between points A and C.
b) Calculate the resistance if you connect your resistance
meter between points A and B.
15. You are given a 20ohm, 1.0mA full-scale galvanometer
and a 1Mohm resistor. Put the resistor in series to make a meter.
a) Is the meter an ammeter or a voltmeter?
b) What is its full scale reading?
c) What is the meter's net resistance?
d) What is the total power dissipated by the meter when it is reading full
scale?
16. You are given a 22
18. An ideal capacitor will hold its charge indefinitely.
However, the charge on an actual capacitor may leak out because of a conducting
path which resembles a resistor in parallel to the capacitor. Consider
a 220microF capacitor which has a time constant of 24hr, initially charged
to 12V.
a) What value of resistance will give a time constant
of 24hr?
b) Fill out the folowing table with the values given
at the times given.
t=0
t=108hr
t=infinity
VR
VC
I
Q
19. The metal in a lm wire has a resistivity of 30mW×
m.
a) What must be the radius of the wire in order to have R=20W?
b) The wire is connected to a 35mF capacitor. Find the time it takes for the capacitor to charge to 63% of its final charge when connected to a 12V battery?
c) What is the current through the wire at the time you calculated in (b)?
20. An ideal capacitor will hold its charge indefinitely. However, the charge on an actual capacitor may leak out because of a conducting path which resembles a resistor in parallel to the capacitor. Consider a 220mF capacitor which has a time constant of 24hr, initially charged to 12V.
a) What value of resistance will give a time constant of 24hr?
b) For t=0, 108hr, and infinity, calculate VR, VC, I, and Q.
21. A 12V battery charges a 100mF capacitor through a 10kW resistor.
a) How long does it take for the capacitor to charge to 95% of its final value?
b) What is the charge on the capacitor after one time constant?
c) If it is a parallel-plate capacitor, with the plates separated by 0.01mm, what is its dipole moment after it is fully charged?
22. A 9V battery is connected to an uncharged 0.1mF capacitor and a 20MW resistor.
a) What is the initial current when the circuit is initially closed?
At t=1 second, what are
b) the current in the circuit?
c) the charge across the capacitor?
d) the voltage across the resistor?
e) the voltage across the capacitor?
23. Sketch the following voltages vs time:
a) VR for a charging RC circuit
b) VR for a discharging RC circuit
c) VC for a charging RC circuit
d) VR+VC for a discharging RC circuit
24. A 330pF capacitor is connected to a 15V power supply.
a) Calculate the charge on either plate when the capacitor is fully charged.
b) If charge is allowed to flow from one plate thrgugh a ll0kW resistor to the other plate, what is the current the instant that this connection is made?
MAGNETISM:
2. In a TV set or computer display, electrons are fired
at the screen from behind. These charges in motion can be thought of as
a current, so describe the direction of the magnetic field they create,
as viewed by someone watching the screen.
3. One microamp flows along the x-axis from x=¥
to x=-¥
. 3mA flows along the z-axis from z=¥
to
z=-¥
. What are the x, y, and z components of the magnetic field at x=30cm, y=40cm, z=0?
4. This paper forms the xy plane. Consider a wire at x=y=0 carrying 5A into the paper, and another wire at x=-20cm, y=0, carrying 3A out of the paper. Calculate the magnitude and direction of the magnetic field at a point P, at x=0, y=20cm.
6. A wire of 0.33m length carries a current of 2A.
a) Calculate the magnitude of the magnetic field at a
distance of 4cm from the wire.
b) Show, on a diagram the direction of the magnetic field.
c) If another wire of the same length, located 4cm away,
also carries 2A and the current runs in a direction parallel to the current
in the other wire, what is the force on this second wire? Is it attracted
or repelled from the first wire?
7. The Earth's magnetic field is created by current flowing
inside.
a) If these currents flow like current in a loop, and
if the crust has a radius of 3Mm, and if the magnetic field is about 50microT
in the center of the loop, how much current is flowing inside the Earth?
b) How fast must an electron (q=-1.60×10-19C,
m=9.11×10-31kg) travel at the Earth's surface for the
maximum magnetic force on it to equal its weight?
8. A compass needle with a magnetic dipole moment of 0.13Am2
sits inside a circular coil of 150 loops of wire arranged with a radius
of 18cm.
a) What field is needed to provide a torque of 0.12Nm
to the needle?
b) What current will produce this field?
c) Draw a figure of how the coil must be situated if
the compass lies flat on the top of a desk and the torque is sufficient
to twist the needle to point East.
9. The power cord of a light bulb consists of two wires
of 1cm diameter located 2cm apart.
a) If the toaster draws 2A of current, what is the magnetic
field at one of the wires, caused by the current in the other?
b) What is the force between two 60cm segments of the
wire?
10. A 2.3A current flows through two identical parallel wires. If the current flows due East in both and one wire is 0.3m North of the other,
a) Give the magnitude and direction of the magnetic field due to the North wire at the location of the South wire.
b) Give the magnitude and direction of the force per unit length on the South wire due to the Northern one.
11. Consider a 15cm diameter coil of 100 loops of wire lying in the plane of this page, carrying a current of 2A (traveling clockwise). A straight wire running from left to right, also in the plane of the page, carries 1A.
a) What is the magnetic field in the center of the coil?
b) What is the magnitude of the force on the straight wire? You may assume that the magnetic field due to the coil is uniform inside the coil, and that it is zero outside the coil.
c) What is the direction of the force on the straight wire?
12. You are standing 10m underneath a single 700kV, 100MW power line, in which the current is flowing to the East. You are also facing East.
a) What is the magnitude of the magnetic field at your location due to this current?
b) Does this field point up, down, to your left or right, or ahead of or behind you?
c) What magnitude force would a 1km length of this wire feel due to a local magnetic field of 50mT pointing 60°
below North?
2. A square loop of wire sits flat on top of a table. If there is a magnetic field inside the loop that points straight up, describe the current (as viewed from someone looking down on the loop) that is induced in the coil if the coil is quickly 'squished' to zero area.
3. A circular coil lies in the plane of this page. A current I1 flows counterclockwise in this coil. A long straight wire, situated above the plane of this page, passes above the center of this coil, with its current, I2, travelling toward the top of the page. What is the direction of the resulting force on the straight wire?
4. Current in a long straight wire travels from left to right in the plane of this page. A magnetic field points from the lower lefthand corner of this page toward the upper righthand corner. If the current is caused by negatively charged electrons, what is the direction of the force on the wire?
5. An iron bar sits atop two metal rails in the plane
of this page that are joined in a semicircle on the right hand side so
that the rail and the iron bar form the letter D. A magnetic field points
out of the page.
a) Which direction does the induced E-field in the bar
point if the iron bar is dragged to the right?
b) Is the induced current in the bar and rails clockwise
or counterclockwise?
6. Current flows to the right in a wire in the plane of
this page. A circular loop of wire, also in this plane, is closer to the
bottom of the page.
a) What is the direction of the magnetic field inside
the loop, produced by the current in the wire?
b) If the current is suddenly decreased, is the induced
current in the wire clockwise or counterclockwise?
7. Two wires lie parallel to the plane of this page. In
one, the current, I1, flows from left to right. The other wire
lies below it, with the current, I2, flowing from the bottom
lefthand corner to the top righthand corner.
a) What is the direction of the magnetic field due to
I1 as felt by the wire carrying I2?
b) What is the direction of the resulting force on I2
due to I1?
9. The magnetic field on planet X is estimated to be 0.03T,
600 times larger than on the Earth, and is found to point 70o
above the horizon.
a) What is the magnitude of the force exerted by the
filed on a 1km long vertical power line on Planet X, which carries 100A
of current?
b) If the 1km stretch of wire is folded into a single
square loop, what is the magnetic moment of this loop?
c) If the loop lies flat on the ground, calculate the
effect of the B-field on it.
10. A turbine converts the rotary motion of a loop of
wire into a 60Hz AC signal. At some instant in time, the normal of the
loop is at an angle of 30o relative relative to a constant magnetic
field. The loop has 20 turns of wire on a 0.35m2 frame, and
sits inside a 1.7T field.
a) What is the magnetic flux in the loop?
b) If the coil is rotated so that the normal is at an
angle of 45o a time 0.69ms later, what is the average induced
voltage during this time period?
c) If the coil has a resistance of 100ohm , what is the
average current that the turbine can generage in this time interval?
11. A coil consisting of 350 loops sits in the plane of
this paper with a magnetic field pointing out of the page. The coil has
a diameter of 10cm and a total resistance of 200ohm. The magnetic field
increases from 2T to 3T.
a) How quickly must the field change in order to produce
a 1mA current in the coil?
b) What is the direction of the current?
12. Consider a 15cm diameter coil of 100 loops of wire
lying in the plane of this page, carrying a current of 2A (traveling clockwise).
A straight wire running from left to right, also in the plane of the page,
carries 1A.
a) What is the B-field in the center of the coil?
b) What is the magnitude of the force on the straight
wire? You may assume that the magnetic field due to the coil is uniform
inside the coil, and that it is zero outside the coil.
c) What is the direction of the force on the straight
wire?
13. A 10cm radius coil sits in the plane of your paper on top of a long wire heading East (to the right of your page).
a) If a current of 3.7A flows clockwise through the loop, what is the magnitude and direction of the magnetic field at the section of the wire below the center of the loop?
b) What is the magnitude and direction of the force on the 20cm length of wire fight below the loop if its current is 2. 1 A due East? (Assume the field inside the coil is uniform.)
14. A coil of wire of radius 10cm lies in the plane of your paper. A 0.95T field points into the paper.
a) What is the magnitude of the magnetic flux through the coil?
b) If the coil is squashed to zero area within 0.5s, what is the induced voltage?
c) If the coil is rotated 200 in 0.05s, what is the induced voltage?
d) What is the direction of the current that flows in this loop in part (c)?
15. A coil consisting of 350 loops sits in the plane of this paper with a magnetic field pointing out of the page. The coil has a diameter of l0cm and a total resistance of 200W. The magnetic field increases from 2T to 3T.
a) How quickly must the field change in order to produce a lmA current in the coil?
b) What is the direction of the current?
16. A 2.03A current travels through a horizontal power line 10.2m above your head, with the current flowing from West to East.
a) Determine the direction of the magnetic field at your location. Be specific: don't answer 'left' or 'right', but rather 'up', 'down', 'North', 'South', 'East', 'West', or something similar.
b) What is the magnitude of the magnetic field at your location?
c) If you are holding a 1m2 coil of 3 windings and 0.023 ohms, so that the coil is in a horizontal plane, 1.02m below the wire, what is the magnetic flux through the coil?
d) What is the maximum average current you can induce through this coil by rotating its position in 1 second?
17. A 4cm diameter coil of 30 windings sits in the plane of this page. A magnetic field of 2.0T faces into the page. The B-field is increased to 3.4T, inducing a 0.030A current in the coil.
a) What is the direction of the induced current?
b) How quickly was the field increased, if the coil has a resistance of 0.32 ohms?
c) What is the magnetic field at the center of the coil due to this induced current?
18. Consider a circular coil in the plane of this page. A current, I2, travels counterclockwise in the coil. A current, I1, travels from left to right in a straight wire above the coil (between you and the coil).
a) What is the direction of the force on the segment of the straight wire directly above the coil?
b) If I1 increases, does the induced current in the coil travel clockwise, counterclockwise, or is there no induced current?
AC CIRCUITS:
1. Line voltage is about 110V at 60Hz in the US and Canada.
a) What is the maximum voltage that comes out of the
wall socket at any instant of time?
b) What is the resistance of a 4-slice, 1600W toaster?
c) What is the capacitance that will allow the same current
to flow when plugged into the wall socket?
2. (Multiple choice) Consider a DC power source in series
with a switch, a resistor, an inductor, and a capacitor. Close the switch.
The final value of current (as t goes to infinity)...
a) depends only on the resistor
b) is zero because of the capacitor
c) is large becasue of the inductor
d) is resonant
e) depends on R, L, and C
3. A 100ohm resistor is connected to a 60Hz power supply.
The power supply has a peak voltage of 35V.
a) What are the peak and rms values of the current?
b) What are the peak and average values for the power
dissipated by the resistor?
c) What inductance could one substitute for the resistor
and get the same current flow?
4. An 8ohm speaker is driven by a 50W amplifier.
a) What is the peak current in the speaker?
b) What size capacitor will give the same peak current
at 60Hz?
c) What size inductor will give the same peak current
at 60Hz?
5. What is the root-mean-square of the following voltages: 0V, 10V, -10V, 0V, -5V, 5V?
6. An 8
16. Electric power is sent long distances over 700kV power
lines.
a) Is 700kV the amplitude, the peak-to-peak, or the rms
voltage?
b) Calculate the other two quantities referred to in
part (a).
c) If a particular 700kV power line carries power from
a 1GW power plant to consumers whose outlets are at 120V, how much total
current do the consumers use? Transformers convert the 700kV to 120V.
d) How many residential customers (limited by their 150A
fuse boxes) can this power plant serve?
17. A 3GW power plant is to 700kV power lines, which are
connected to transformers that step it down to 110V.
a) What is the peak voltage across the power lines?
b) What is the maximum instantaneous power delivered
by the power lines?
c) What is the average power delivered by the power lines?
d) What is the turns ratio of the transformers?
e) What is the total current delivered to the customers?
18. A 3GW power plant is connected to 700kV power lines, which are connected to transformers that step it down to ll0V.
a) What is the peak voltage across the power lines?
b) What is the maximum instantaneous power delivered by the power lines?
c) What is the turns ratio of the transformers?
d) What is the total current delivered to the customers?
19. Consider an AC transformer which converts 120V to 6V, and which has 20 coils on the secondary.
a) How many coils does the primary have?
If the secondary delivers 0.20A to some resistor,
b) what is the maximum current at the primary? The rms current?
c) What is the maximum power consumption at the resistor?
20. A 12V car battery has been connected to the primary of a transformer with a turns ratio of 20:1 (primary turns to secondary). After the system achieves a steady-state condition, one measures 3A flowing through the primary windings.
a) What is the voltage across the secondary windings?
b) What is the current flow through the secondary?
The battery is replaced with an AC voltage with 120V peak voltage. The maximum current flow in the primary is 3A.
c) What is the rms current through the secondary?
GEOMETRIC OPTICS
1. (Multiple choice) How long should it take light to
travel the distance between the U.S. and Europe (about 5000km) underwater?
The index of refraction for water is about 1.33.
_____22ms_____17ms_____17ms_____13ms_____10ms
2. A physics student stands with her eyes 1.8m above the
ground at one end of a lake. On the opposite shore, 700m away, stands a
tree.
a) If an image of the top of the tree appears in the
lake at an angle 4.2o below the horizon, how tall is the tree?
b) What is the angle of refraction of this image of the
treetop as it enters the water at point P if n=1.33 for water?
3. I am looking at a fish swimming below the surface of
a lake.
a) If the light entering my eye from the fish travels
at an angle of 60o above the horizon in the air, at what angle
does that ray travel under the water? The index of refraction for water
is 1.33.
b) Sketch two rays leaving the fish at this angle and
exiting the surface of the water.
c) If the fish appears to be 25cm below the water's surface,
how far below is it really? Find where the two rays leaving the water in
part (b) would meet if you followed them back below the surface. This is
where the fish appears to be.
4. Light enters a prism perpendicular to one face, and
hits the next surface with an incident angle of 30o.
a) What is the angle between the two prism faces? (this
is known as the apex angle of the prism.)
b) The ray of light enters the air again at an angle
15o away from the direction it entered the first surface. What
is the index of refraction in the prism?
c) For a different wavelength of light, the index of
refraction is exactly 1.500. How much is the incident beam deflected by
going through the prism?
5. A piece of optical fiber consists of a cylindrical 'core' inside a concentric cylinder of 'cladding'. This particular fiber has a numerical aperture of 0.20, meaning that rays entering the core from the end of the fiber at angles less than q such that sinq=0.20 will travel through the core and always be reflected at the boundary with the cladding. The index of refraction of the core is exactly 1.5.
a) At what angle, relative to the axis of the fiber, do rays travel inside the core?
b) At what angle, relative to the normal, do these rays reach the cladding?
c) What is the index of refraction of the cladding? Include enough significant figures to distinguish your answer from 1.5.
6. Light enters a prism perpendicular to one face, and hits the next surface with an incident angle of 30°.
a) What is the angle between the two surfaces? (this is known as the apex angle of the prism.)
b) The ray of light enters the air again at an angle 5° away from the direction it entered the first surface. What is the index of refraction in the prism?
c) For a different wavelength of light, the index of refraction is exactly 1.500. How much is the incident beam deflected by going through the prism?
7. Ulexite, a clear borate mineral which crystallizes in a fibrous form resembling a bundle of optical fibers, has an index of refraction which depends on the direction of travel (and polarization). Along its three axes, n=1.491, 1.504, and 1.521. The speed of light in a vacuum is 2.9979´
108m/s.
a) What is the fastest that light can travel inside ulexite?
b) What is the longest amount of time light can take to travel 3mm in ulexite?
c) If light travelling in the 1.521 direction hits the boundary with another crystal for which n=1.491, what angle in the first material leads to total internal reflection?
8. Two kids standing at the edge of a pier are dropping identical stones in a pond 3m apart every 2 seconds. The waves from the stones travel at 1.3m/s.
a) What is the wavelength of the disturbances caused by the stones?
b) At what angle(s) (relative to a line perpendicular to the pier) is the water least disturbed by the stones (i.e. the ripples are smallest in amplitude)?
c) If the kids continue to drop stones at the same frequency, but alternate, so that one stone is dropped by a kid every second, would the water in the direction perpendicular to the pier be calm or "choppy"?
10. An object is held 50cm away from a lens which forms
a virtual image 37cm from the lens on the same side of the lens as the
object.
a) What is the focal length of the lens?
b) Is this a converging lens or a diverging lens?
c) What is the magnification of the object?
11. Which of the following are true? (more than one answer)
_____ Lenses work because of refraction.
_____ Refraction occurs because the speed of light is
different in different media.
_____ It is impossible for a diverging lens to create
a real image from a real object.
_____ It is impossible for a converging lens to create
a virtual image.
_____ The focal length of a convex mirror is positive.
12. How many of the following are true? (There is more than one answer.)
_____ Lenses work because of refraction.
_____ Refraction occurs because the speed of light is different in different media.
_____ It is impossible for a diverging lens to create a real image from a real object.
_____ It is impossible for a converging lens to create a virtual image.
_____ The focal length of a convex mirror is positive.
13. What is the focal length of a magnifying glass that produces a magnification of 4.00 when held 7.00cm from an object? Show a ray diagram (with all of the principal rays), and solve exactly.
14. A shopper standing 5.00 m from a convex security mirror sees her image with a magnification of 0.333. (a) Where is the image?
(b) Solve for the focal length of the mirror exactly, and show all of the principal rays in a ray diagram.
15. Another car is 20m behind yours. The rearview mirror creates a virtual image of this car which is 30m in front of your car.
a) Draw a ray diagram and trace the three principal rays.
b) What is the focal length of this mirror?
c) What is the magnification of the mirror?
17. A nearsighted patient has a far point of 1.3m.
a) Calculate the focal length of the appropriate corrective
lenses for the patient.
b) Calculate the strength of these glasses.
c) If the patient's uncorrected near point is 12 cm,
what is it with the glasses on?
18. An optometrist prescribes you a pair of glasses of -6.00 diopters. What condition will these glasses correct? If the glasses listed above replace your old prescription of -6.10 diopters, are your eyes getting better or worse?
19. A newborn is said to be able to focus on objects about
30 cm away.
a) If this is his far point, prescribe glasses for him,
assuming that he wants to be able to read the newspaper, 25cm away.
b) If the baby's eyeball is 2.5 cm from front to back,
what is the focal length of his eyeball when he focuses at an object 30
cm away, it if causes an image to form on the back of his eyeball?
20. Answer true or false these questions about optical
systems:
a) _____ Nearsightedness may be due to having too strong
a lens in one's eye.
b) _____ Farsightedness may be due to having too short
an eyeball.
c) _____ For a magnifying glass, the angle subtended
by the object on the retina is the same as the angle subtended by the image
on the retina.
d) _____ The image made by the objective of a microscopy
is the best object for the eyepiece.
e) _____ Magnifying glasses or microscopes work by bringing
images as close as possible to the eye.
21. A magnifying glass is used to look at a grasshopper.
a) If it says "8×" on the magnifying glass, and
if it is used to put an image of the insect at your focal point, then how
much larger will this image be than the object?
b) What is the focal length of the lens?
c) If your near point is at 25 cm, then how close must
the insect be to the glass to get the image to appear at your near point?
22. A normal human can focus on objects between about
25cm and infinity.
PHYSICAL OPTICS:
2. A beam of 3cm microwaves hit a metal screen with two
vertical 5cm wide slits in it. The slits are side-by-side and have a 5cm
divider between them. Microwaves are a form of electromagnetic radiation,
and are reflected by metals.
3. Answer the following true/false questions:
4. Answer true or false these questions about physical
optics:
5. Light enters a prism normal to one surface and leaves
another surface tilted 30o with respect to the first surface.
The index of refraction for red light (700 nm) is 1.334.
6. Consider the note "A" (f = 440 Hz) entering an acoustically
insulated room (no echoes) from two doors. Each door is 1.2m wide.
Sound travels from the doors to a stage 20m away. The speed of sound in
the room is 340 m/s.
7. Which of the following effects (more than one answer)
reveal the wave nature of light?
8. A diffraction grating has 5000 lines per cm.
9. Circle each of the following which are examples (or
results) of Rayleigh scattering:
10. Two 1-m wide doorways in a physics lecture room are
located with their centers 6m apart. A stereo in the hallway plays
a work by Philip Glass which consists of a 980 Hz tone repeated over and
over.
11. A microscopic layer of some transparent material with
an index of refraction of 1.50 sits on the surface of a lake (n=1.33).
RELATIVITY:
2. Answer true or false these questions about relativity:
3. Answer true or false these questions about relativity:
4. An astronaut Larry, aged 20, leaves his twin Laura
on earth while he travels to Alpha Centauri, from which it takes light
4 years to travel. Larry wants to get there and back for Laura's 30th birthday,
so he travels at 0.8c.
5. If the Sun were an inertial reference frame, would
the Earth also be one? Would the Moon? Explain.
6. The Klingons are chasing the Starship Enterprise at
0.7c, relative to a nearby planet, while the Enterprise is travelling at
0.6c relative to the same planet.
7. Two astronauts, Pat and Mike, pass each other in identical
spaceships. Pat sees the Moon approaching her ship at 0.90c, and
Mike approaching at 0.99c.
8. A spacecraft travels between Earth and Mars.
Which observer -- one on Earth or one on the spaceship -- will measure
the 'proper time' for the length of the trip? Which one measures
the proper length for the distance between the planets?
9. The oppossum ('marsupialis virginiania', for example)
is about 90 cm long and lives only about one year, owing to its almost
total lack of defense against predators. The raccoon ('procyon lotor')
has a length of about 83 cm and lives an average of about 10 years.
(Hence the expression -- "I ain't seen you in a 'coon's age.')
10. An Earthside observer, Pat, watches an astronaut,
Mike, pass by in a spaceship. Meanwhile a missile is fired from Earth.
What variable names would you give each of the following quantities?
(No equations, please!)
11. Two spaceships approach the Earth from opposite directions.
If each one approaches the Earth at 0.9c, their relative speed is
12. Two spaceships approach each other at 0.95c.
Spaceship A is traveling at 0.8c relative to a nearby planet.
13. The new Air Force F32 bomber cruises at 0.01c. Its
manufacturer says that this speedy number is exactly 10m long and has exactly
8000kg mass.
MODERN PHYSICS:
a) Calculate maximum and minimum values of the strength
of the eye's lens, given that an image is formed on the retina 2.5 cm behind
the lens?
b) By what percentage does the strength change during
accommodation?
23. Your instructor is badly myopic and needs -8D glasses to see well.
a) How far can he see clearly without the glasses?
b) What is his uncorrected near point if his corrected near point is 25cm?
c) Draw a ray diagram for this last case, showing the principal rays, the object and image.
24. A nearsighted person has an uncorrected near point of 12cm and an uncorrected far point of 25cm.
a) What will the patient's prescription read? (What quantity, units, etc.?)
b) When the patient is wearing her new glasses, what range of distances can she focus on? (from what distance to what distance?)
25. You are an optometrist. A patient comes into your office requiring bifocals. The strength of the lenses are +l.5D and -1.5D.
a) What is your patient's uncorrected near point?
b) What is your patient's uncorrected far point?
1. Fill in the blanks with an appropriate choice. (There
may be more than one correct answer.)
The phenomenon of ______________ is the most compelling
demonstration that light is a transverse wave.
The process by which the eye changes its 'focus' is called
_________________.
Reflected light is shifted 180o when ________________________________________________.
a) If one of the slits was covered, what would be the
angular width of the central diffraction maximum?
b) How many interference maxima are there? (Be sure to
include the zeroth maximum if there is one, and maxima on both sides of
it.)
c) How many interference maxima are there inside the
central diffraction maximum? (Include maxima on either side of the center,
and include the center if appropriate. Include the maximum at the edge
of the central diffraction maximum, if there is one.)
_______Rainbows are examples of Rayleigh scattering.
_______If unpolarized light enters a polarizer, the intensity
of transmitted light is independent of the angle at which the polarizer
is held.
_______Colors observed in looking at soap bubbles are
examples of dispersion.
a) _____ Clouds ar white because of Rayleigh scattering.
b) _____ If unpolarized light enters a polarizer, the
intensity of light leaving the polarizer depends on the angle at which
the polarizer is held
c) _____ The positions of the intensity maxima from a
many-slit interference pattern are the same as the positions of the maxima
from a two-slit pattern.
d) _____ One does not hear intensity maximum and minima
from two audio speakers less than, say, 10m because the interference maxima
would be too close together.
e) _____ One does not see diffraction around a picket
fence because the spacing between the pickets is too big.
a) At what angle (relative to the second normal) does
the light leave the second surface?
b) What must be the index of reflection for violet light
(400 nm) in order for it to be bent 5o more than the red?
c) What would be the distance between lines in a diffraction
grating in order to give the same angular distance between red and violet
in the first-order maxima? (Notice: for such small angles, sinA -
sinB = sin(A-B).)
a) What is the wavelength of the sound?
b) What is the width of the central diffraction maximum
on the stage?
c) If the fifth interference maximum is also the second
diffraction minimum, then what is the distance between the centers of the
two doors?
_____ Polarization_____ Dispersion _____ Diffraction
_____ Interference _____ Refraction
a) At what angle is red light of 650 nm wavelength bent
for the first interference maximum?
b) How many such maxima would occur between 0o
and 90o?
a) clouds.......................................................b)
the sky on a cloudless day
c) your exhaled breath on a cold day............d) red
sunsets
a) If one door is closed, and if we can ignore
reflections, what is the smallest angle from the other doorway where you
can sit and hear nothing? The speed of sound is about 340 m/s.
b) If both doors are open, what is the smallest angle
at which you could sit and hear nothing?
a) Does this system resemble an 'oil slick' or a 'soap
bubble' as far as interference effects are concerned?
b) If the layer were perfectly thin, how would
it appear if you looked at it at normal incidence? (What kinds of light
would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will
have some colored sheen to it. If green, 550nm light is seen in normal
reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (c), what
visible wavelengths, if any, will destructively interfere on normal reflection?
12. Light of 280
a) At what angle is the first dark diffraction band?
b) Which interference maximum or minimum (state which one) occurs at this angle?
c) How many bright interference bands occur within the 'central diffraction maximum'? Don't include the answer to part (b), even if it qualifies as a bright band.
13. A microscopic layer of some transparent material with an index of refraction of 1.50 sits on the surface of a lake (n =1.33).
a) Does this system resemble an 'oil slick' or a 'soap bubble' as far as interference effects are concerned?
b) If the layer were perfectly thin, how would it appear if you looked at it at normal incidence? (What kinds of light would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will have some colored sheen to it. If green, 550nm light is seen in normal reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (b), what visible wavelengths will perfectly destructively interfere on normal reflection?
14. Fill in the blanks with an appropriate choice. (There may be more than one correct answer.)
The phenomenon of________________is the most compelling demonstration that light is a transverse
wave.
The process by which the eye changes its 'focus' is called_______________.
Light is shifted 180° when it reflects off___________________.
15. A beam of 3cm microwaves hit a metal screen with two vertical 15cm wide slits in it. The slits are side-by-side and have a l0cm divider between them. Microwaves are a form of electromagnetic radiation, and are reflected by metals.
a) If one of the slits was covered, what is the width of the central diffraction maximum on a screen lm away?
b) How many interference maxima are there? (Be sure to include the zeroth maximum if there is one, and maxima on both sides of it.)
c) How many interference maxima are there inside the central diffraction maximum? (Include maxima on either side of the center, and include the center if appropriate. Include the maximum at the edge of the central diffraction maximum, if there is one.)
16. Answer the following true/false questions:
--Rainbows are examples of Rayleigh scattering.
--If unpolarized light enters a polarizer, the intensity of transmitted light is independent of the angle at which the polarizer is held.
--Colors observed in looking at soap bubbles are examples of dispersion.
17. A microscopic layer of some transparent material with an index of refraction of 1.65 sits on the surface of a lake (n=1.33).
a) Does this system resemble an 'oil slick' or a 'soap bubble' as far as interference effects are concerned?
b) If the layer were perfectly thin, how would it appear if you looked at it at normal incidence? (What kinds of light would reflect off it well, which would not reflect well)?
c) If the layer instead has a finite thickness, it will have some colored sheen to it. If red, 650nm light is seen in normal reflection off the film, what is the minimum thickness of the layer?
d) For the same thickness as calculated in (c), what visible wavelengths, if any, will destructively interfere on normal reflection?
18. A pair of slits produces a light pattern on a distant screen which is a combination of 2-slit interference and single-slit diffraction. Describe one attribute of the pattern that is a result of interference and one attribute which is the result of diffraction. How can one tell by looking at the pattern that the slit separation is larger than the individual slit widths?
19. A beam of 4cm microwaves hit a metal screen with two vertical 5cm wide slits in it. The slits are side-by-side and have a 10cm divider between them. Microwaves are a form of electromagnetic radiation, and are reflected by metals.
a) If one of the slits was covered, what would be the angular half-width of the central diffraction maximum?
b) How many interference maxima are there? (Be sure to include the zeroth maximum if there is one, and maxima on both sides of it.)
c) How many interference maxima are there inside the central diffraction maximum? (Include maxima on either side of the center, and include the center if appropriate. Include the maximum at the edge of the central diffraction maximum, if there is one.)
20. A layer of water (n2=1.33) sits on a glass slide (n3=1.50).
a) Does this system behave as a "soap bubble" or an "oil slick"? Why?
b) If the layer of water is exactly one micron thick, what visible wavelengths (400-700nm) will reflect most intensely?
c) What visible wavelengths will reflect least intensely?
21. 632.8nm HeNe light is incident on a single slit of width 1.5mm.
a) At what positive angles, q, relative to the stit does a dark band occur?
b) If a pattern of bright and dark fringes is observed on a screen 10cm form the slit, how wide is the central bright fringe on the screen?
1. Two spaceships approach each other as each passes
a nearby planet at 0.99c, that is, the speed of each spaceship relative
to the planet is 0.99c.
a) At what speed do these ships approach each other?
b) The pilot on spaceship A is dieting, and measures
him/herself to be about 70kg. What do the people in spaceship B measure
for the dieting pilot's mass?
c) The same pilot is 25cm thick from front to back. What
do the passengers on the other spaceship measure, assuming the pilot is
facing in the direction of travel?
d) Energy and mass are equivalent, so we can express
energy in terms of rest mass. How much energy must have been exerted at
some point to accelerate this spaceship from rest on the nearby planet?
Please give your answer in units of moc2, the rest
energy.
a) _____ If an astronaut travels toward a distant star
at 0.99c, she will observe her twin who remains on Earth appear to age
less rapidly than she.
b) _____ If an astronaut travels toward a distant star
at 0.99c, her twin who remains on Earth will observe her to age less rapidly
than she.
c) _____ One implication of Einstein's second postulate
is that, if you shine light through water, its speed will be independent
of whether the light is moving.
d) _____ The starship Enterprise hurtles through space
at 0.999c. It would be common for people to celebrate their 300th birthdays,
given today's medical technology.
e) _____ There is no inertial reference fram for which
a meter stick appears twice as long.
a) _____ The Earth is, strictly speaking, not an inertial
reference frame.
b) _____ If we could speed up a clock to travel at the
speed of light, it would appear to a stationary observer to not be running.
c) _____ There exists an inertial reference frame in
which you would hear the sound of a baseball hitting a ball before you
would see it.
d) _____ If a 4m long car travels through a 4m long garage,
a person in the garage sees the car as shorter than the garage. (The
car fits inside.
e) _____ If a 4m long car travels through a 4m long garage,
the driver sees the garage as shorter than the car. (The car doesn't
fit inside.)
a) How far does Larry measure the distance to Alpha
Centauri?
b) How much older is Larry when he returns?
c) Larry and Laura remain in radio contact.
How much faster or slower does Larry observe Laura's clocks to be running?
d) From part (c), what would Larry expect Laura's
age to be when he returned, given the rate of Laura's clocks? (The difference
between this number and 10 years is accounted for by the fact that as Larry
turns around at Alpha Centauri, he has to accelerate, and so is no longer
in an inertial reference fram. During the time it takes him to turn
around, Laura ages quite rapidly.
a) How fast do the Klingons measure themselves to be
closing in on the Enterprise?
b) An observer on the planet measures the distance between
ships to be 5 light minutes. How far do the Klingons measure it ot
be?
c) How long do the Klingons measure for the time needed
to catch the Enterprise and how long do the 'ground observers' measure?
a) For Pat, what is the ratio of the height of
the Moon to its width?
b) What is the speed of Mike's vessel, relative
to the Moon?
c) If Pat measures her vessel to be 300m long,
how long will Mike measure it to be?
a) If a ground-based raccoon sees a spaceship full of
'possum that seem to have a mean lifespan befitting a raccoon, how fast
is the spaceship moving relative to the ground?
b) What length does the 'coon measure for the typical
length of a 'possum? (Neither animal is particularly noted for its
eyesight.)
c) What is length of the raccoon as viewed from the spaceship?
a) Mike's velocity as measured by Pat
b) the velocity of the missile as measured by Mike
c) Mike's measurement of his own ship
a) zero................b) between zero and 0.9c..................
c) between 0.9c and c...............d) between c and 1.8c.......e) 1.8c
a) What is the velocity of Spaceship B, relative to the
planet?
b) The science officer aboard Ship A measures the ship's
mass to be 2.3 × 107 kg. What does her colleague
on the planet measure for Ship A's mass?
c) The chief engineer on Ship A measures Ship B to be
24m long. What does someone on Ship B measure for its length?
a) What does ground control measure for its length when
it is flying overhead?
b) What does ground control measure for its mass when
it is flying overhead?
c) What is its kinetic energy? (Do not use the classical
formula)
d) If the bomber uses a matter-antimatter drive which
converts directly into energy, how much mass needed to be converted to
achieve its final kinetic energy?
14. Two spaceships approach Earth from opposite directions, each travelling at 0.5c relative to the Earth.
a) At what rate are the two spaceships approaching each other?.
There are three observers in this problem, the captain of one ship, the captain of the other ship, and an observer on the Earth. Each spaceship is manufactured to be 300m long.
b) Which observer measures the longest length for the length of the ship? How long is that?
c) Which observer measures the shortest length for the ship? How long is that?
15. One object of lkg slams into another object at rest. The first particle goes from travelling at 0.9c to the right to travelling at 0.5c to the right. The second object ends up travelling at 0.4c to the right
a) What is the initial momentum of the first object?
b) What is that object's total initial energy?
c) What is the mass of the second object, if the total momentum is conserved?
16. The new Air Force F32 bomber cruises at 0.01c. Its manufacturer says that this speedy number is l0m long and has an 8000kg mass.
a) What does ground control measure for its length when it is flying overhead?
b) What does ground control measure for its mass when it is flying overhead?
c) What is its kinetic energy? (Do not use the classical formula)
d) If the bomber uses a matter-antimatter drive which converts directly into energy, how much mass needed to be converted to achieve its final kinetic energy?
17. Two spaceships approach each other as each passes a nearby planet at 0.99c, that is, the speed of each spaceship relative to the planet is 0.99c.
a) At what speed do these ships approach each other?
b) The pilot on spaceship A is dieting, and measures him/herself to be about 70kg. What do the people in spaceship B measure for the dieting pilot's mass?
c) The same pilot is 25cm thick from front to back. What do the passengers on the other spaceship measure, assuming the pilot is facing in the direction of travel?
d) Energy and mass are equivalent, so we can express energy in terms of rest mass. How much energy must have been exerted at some point to accelerate this spaceship from rest (relative to the planet)? Please give your answer in units of moc2, the rest energy.
18. Two identical space utility vehicles, built to specifications of 91.4m and 43000kg, find themselves approaching on Intergalactic Highway I90. Your vehicle is doing 0.6c (relative to the Earth), which is the legal speed limit on the expressway in congested areas. Your laser Doppler meter gives the approaching craft's speed as 0.9c.
a) Is the approaching craft violating the speed limit? What is its speed, relative to the Earth?
b) What does your navigation system measure for the other craft's length and mass?
c) What does the other craft measure for your length and mass?
d) Which craft does an observer on Earth measure as shorter, and which as heavier?
19. A 2kg mass is accelerated by a constant 3N force. What is the acceleration of the object when v=0.9c?
20. A space cruiser approaching the Earth at 0.6c fires a nuclear torpedo at New York City. New Yorkers measure the closing speed of the torpedo to be 0.99c.
a) What is the muzzle velocity of the torpedo?
b) If scientists in New York calculate that they have twenty minutes until impact, how much time will elapse on the torpedo's clock between its launch and its landing?
21. Two spaceships approach each other at 0.90c. Spaceship A is traveling at 0.60c relative to a nearby planet.
a) What is the velocity of Spaceship B, relative to the planet?
b) The science officer aboard Ship A measures the ship's mass to be 1.00´
107 kg. What does her colleague on the planet measure for Ship A's mass?
c) The chief engineer on Ship A measures Ship B to be 100m long. What does someone on Ship B measure for its length?
22. A muon is an unstable particle that has a lifetime of 2.20microsecond in its rest frame. If it is travelling at 0.990c relative to the ground,
(a) What does the Earth-bound observer measure for its lifetime?
(b) How far does the muon "think" it travels before disintegrating?
(c) How far does the Earth-bound observer think it travelled?
(d) How can parts (b) and (c) be consistent?
23. Two particles have rest masses of 90MeV/c2 each. Initially, one of them is at rest in the lab frame, and the other is approaching it at 0.5c.
a) What is the rest mass of the particles in MKS units?
b) What is the total initial energy of the moving particle in the lab frame in MeV?
c) Classically, we might imagine the two particles suffering an inelastic collision in which they both move in the same direction with v=0.25c. Show relativistically that this cannot happen.
1. The human body has a temperature of 37°C (310K, 98.6°F). Making the appropriate assumptions about the body,
a) What can you say about the peak region of radiation emitted by the human body?
b) If you run a fever of 103°F (40°C), by what percentage does the amount of radiation emitted by your body increase?
2. The Sun has an inner temperature of about l08K. Its surface temperature is such that its radiant output is in the visible -- let's say 550nm.
a) What is the Sun's surface temperature?
b) The Earth's surface temperature averages about 300K. A global change of about 10K would probably be disastrous to life as we know it. If this change in temperature is due to a decrease in the sunlight hitting the Earth, what percentage decrease would have to occur to see this large a global cooling?
3. Two identical objects are in the same surroundings at 0°
C. One is at a temperature of 500K, and the other is at 400K. Find the ratio of the net power emitted by the hotter object to the net power emitted by the cooler object.
4. In a laboratory experiment designed to duplicate Thomson's determination of e/m, a beam of 6.00´
107m/s electrons enters a 5.00mT magnetic field. The beam moves perpendicular to the field in a path having a 7cm radius of curvature. Determine e/m from these observations. Is this value consistent with the accepted value?
5. In a Millikan oil drop experiment, a 500V potential difference is applied to plates separated by 2.20cm.
a) How many electrons of charge does an oil drop of 1.07´
10-14kg have, if it is suspended motionless between the plates?
b) What is the diameter of the drop, if it has a density of 0.9g/cc?
, how energetic must the alphas be to just barely reach the surface?
atom is 239.05216u.
(163.93920u), 
(63.92796u), and a bunch of neutrons (1.008665u)?57. When x-rays pass through a one-atomic-layer thick gold
foil, the holes between atoms behave like interference slits.
a) If the atoms are 5×10-10m apart,
what wavelength x-ray will cause the first interference maximum to occur
at 100?
b) How many interference maxima will occur between -90o
and 90o?
58. An electron can travel in a straight line in
a) a uniform E-field perpendicular to the electron's
path.
b) an E-field and B-field both parallel to the electron's
motion
c) E-field and B-fields perpendicular to each other and
the electron's motion
d) a uniform B-field perpendicular to the electron's
path
59. TRUE / FALSE
_____ Lasers are more efficient at converting energy
into light than most light sources.
_____ The energy of an electron's orbit decreases
as "n" increases.
_____ "The whole is greater than the sume of the parts",
as far as the mass of nuclei and the masses of neutrons and protons is
concerned.
_____ The density of mass in a nucleus is roughly the
same for 1H as it is for 238U.
_____ Cathode rays are not particles.
60. In Chapters 25-31 we have sometimes had to abandon the laws of classical physics to explain observed phenomena, as happened with Relativity. Cite an instance where the laws of modern physics contradict those of classical physics, and explain why the laws of classical physics are violated.
61. The kinetic energy of a molecule of air at standard
temperature and pressure is about 1/40eV. This is certainly not enough
to ionize a hydrogen atom in its ground state, but it will ionize a more
energetic hydrogen atom.
a) What is the quantum number, n, of the lowest-lying
energy state of hydrogen that can be ionized by 1/40eV?
b) What is the radius of a hydrogen atom in the state
described in (a)?
c) What is the wavelength of a photon produced when an
electron falls from the state given in (a) to the next lower energy state?
62. The proton, m=1.66×10-27 kg, is about
1 fm =10-15m large.
a) If 1 fm represents the uncertainty of the proton's
position, then what is the minimum uncertainty in its momentum?
b) Find the wavelength of a proton traveling at 1% of
the speed of light. (Assume classical dynamics.)
c) Compare the momentum of such a proton with the uncertainty
calculate in (a).
63. When 235U fissions into two nuclei, it releases
about 200 MeV.
a) How many kg of mass is converted into energy?
b) Since such a small fraction of the mass is converted
into energy, almost all of the mass is converted into waste. How
many kilograms of waste is produced in creating 200 MeV?
c) How many kg of waste would be produced in creating
1020J of energy, approximately one year's world energy needs?
64. Answer 10 of the following True/False questions:
a. _____ Electrons are composed of three smaller particles
called quarks.
b. _____ The proton is the electron's antiparticle and
vice versa.
c. _____ Electrons are, as near as can be determined,
pointlike particles having no size.
d. _____ The purpose of the helium in a HeNe laser is
to "optically pump" the neon atoms.
e. _____ A photon incident on an atom in the active medium
of a laser can result in two photons leaving the atom.
f. _____ The coherence of laser light depends on the
nature of the "stimulated emission."
g. _____ The number of hydrogen atoms that could be squeezed
onto the 0.3mm square head of a pin is about 1011, within a
factor of ten.
h. _____ The 4000th excited hydrogen state has a radius
smaller than 1 mm.
i. _____ The energy of the 200th level of hydrogen is
E200= -0.068 eV.
j. _____ For Bragg scattering from a given crystal, decreasing
the wavelength of incoming radiation will decrease the scattering angle.
k. _____ The path of a cathode ray can be bent by a magnetic
field.
l. _____ Two carbon nuclei (Z=6), if fused together,
would give off energy.
65. The isotope 218O has a mass
of 21.008730u. 219F has a mass of 20.999948u. Both
decay by beta emission.
a) What is the binding energy of the oxygen isotope?
If a 21O isotope decayed by beta emission
to 21F,
b) would it be beta+ or beta-?
c) how much energy would be given off or absorbed? (Which?)
66. A neutron star is a stellar object which consists
of a gigantic nucleus composed of neutrons only. Consider such a
star which has a radius equal to the Sun's: r = 7.0 × 108m.
a) What is the atomic mass, A, of this "nucleus"?
b) What is its mass?
c) What is its mass density in kg/m3?
67. Among the more toxic products of the incident at Chernobyl
(1985?) are the following:
90Sr (Z=38) half-life = 28.8 year................
109Cd (Z=48) half-life = 453 days ..................131I
(Z=53) half-life = 8 days
For each radioactive species, calculate the ratio of
its radioactivity today to its radioactivity when originally released.
(Round to the nearest year.)
68. The density of gold is 19.3 g/cm3; its
atomic mass is 197.0g.
a) How many atoms of gold are there in a cubic centimeter?
b) What is the distance between gold atoms?
c) If the distance between atoms were doubled and the
mass of each atom were doubled, how would the density change?
69. A theorist has assigned the up and down quarks each
a mass of 335MeV/c2, and the strange quark a mass of 340 MeV/c2.
a) Calculate the binding energy of a 938.3 MeV/c2
proton (uud), assuming these quark mass values.
b) Calculate the mass defect of a 494 MeV/c2
kaon-plus (An up quark and an 'anti-up' ).
70. The half-life of a neutron (outside of the nucleus)
is 10.6min, after which it decays by beta emission to become a proton.
a) What kind of beta emission is it: positive or negative?
b) How long would one need to wait after entering a room
full of Avogadro's number of loose neutrons before there was approximately
only one left?
c) Give one reason why the reaction n ---> p + beta is
not allowed.
71. Consider the reaction: 2H + 3H
---> 4He + X
a) What is the unknown reaction product, X?
b) How much energy is given off or absorbed in this reaction?
Is it given off or absorbed?
c) What is the binding energy of 4He?
72. Consider Bohr's model of the hydrogen atom. Consider
the third electron energy level. Its kinetic energy equals the magnitude
of the total energy of that state, which is nonrelativistic.
a) Calculate the momentum of the electron in this state.
b) Calculate the uncertainty in the momentum, assuming
the same Delta px=1.41p we used in class for the ground state.
c) Calculate the uncertainty in position, using Delta
x =1.41r, where r is the radius of the electron's orbit.
d) Are the results of (b) and (c) consistent with the
laws of quantum mechanics? Why or why not?
73. Consider the reaction: K - + p ---> Sigma+
+pi-
a) Verify three absolute conservation laws for this reaction.
(Obviously, we don't have enough information to prove for example, momentum
conservation.)
b) How much energy is given off or absorbed in this reaction?
Is it given off or absorbed?
c) Calculate the binding energy of the K -
particle, given its mass in the table below. (In the actual exam, the table
would actually be there.)
74. A 400ng sample of americium is confined to the insides
of a smoke detector. It has been measured using advanced laser Doppler
technology to be moving at less than 1nm/s.
a) Does 1nm/s give us the upper or lower limit for the
americium sample's wavelength?
b) What is that limit? (the wavelength)
c) What is the smallest possible uncertainty in the americium's
position?
76. What range of wavelengths could one get out of a hydrogen-atom laser, if such a thing exists, and if any of the states could be the final state?
77. An upconversion fiber laser has a laser cavity which
consists of a long optical fiber, doped with some optically active material.
Consider a 2m-long fiber laser, which is pumped with 980nm laser light
and which lases at 550nm. The index of refraction of the glass fiber is
1.500.
a) How many half-wavelengths of the 'pump' light fit
inside the length of the fiber?
b) How many half-wavelengths of the laser light fit inside
the length of the fiber?
78. A diode laser has a laser cavity of 0.1mm length and
emits 635nm light. Assume the index of refraction to be 1.40.
a) How many half-wavelengths fit inside the laser cavity?
b) By what fraction would the wavelength change if there
was one fewer half-wavelength? Would it increase or decrease?
c) By how many Hertz will the frequency of the emitted
light change? This is called the 'mode spacing' of the laser.
79. A hypothetical laser emits light of wavelength of exactly 450nm, as measured in a vacuum.
a) This corresponds to an electron transition of how much energy?
b) If the optical resonator of the laser has a length of exactly 10cm and the index of refraction of exactly 1.8, then how many half-wavelengths, N, fit in the resonator?
c) What is the smallest amount by which the resonator could be lengthened and still allow the same exact wavelength to lase?