Name _________________
Test 2
March 19, 2008
This test consists of three parts. Please note that in parts II and III, you can skip one
question of those offered.
Possibly useful formulas:
Constants
e = 1.602 ×10−19 C
ε 0 = 8.854 ×10−12 C2 /N/m 2
μ0 = 4π ×10−7 T ⋅ m/A
RC Circuits
Q = Q0 e −t τ
Q = CE (1 − e
Circles
C = 2π R
A = π R2
−t τ
)
Cyclotro
n Motion
mv = qRB
qB
ω=
m
Loops
τ = IA × B
U = − IA ⋅ B
Triangles
A = 12 BH
Spheres
A = 4π R 2
V = 43 π R 3
Hall Effect
IB
ΔVH =
tnq
Field from Wire
μI
B = 0 ( cos θ1 + cos θ 2 )
4π a
μI
B= 0
2π a
Biot-Savart
μ I ds × rˆ
B= 0 ∫ 2
4π
r
Cylinders
V = π R2 L
Alat = 2π RL
Solenoid
Bin = μ0 NI A
Cones
V = π R2 L
1
3
Alat = π R L2 + R 2
Part I: Multiple Choice [20 points]
For each question, choose the best answer (2 points each)
1. If you have two resistors R1 and R2, and you wish to combine them to make a resistor
with less resistance than either one, you could connect them in
A) series, but not parallel
B) parallel, but not series
C) series and parallel will both work
D) neither series nor parallel will work
E) it is impossible to tell without knowing the specific values of the resistances
2. A superconducting (perfectly conducting) wire loop lies in a region with a magnetic
field passing through it. Suddenly, the wire loop is doubled in size, by stretching the
wires. How does the total magnetic flux through the wire loop change as it increases?
Include any effects caused by currents that begin to flow through the wire loop.
A) The flux gets twice as big
B) The flux gets four times as big
C) The flux gets half as big
D) The flux gets one-fourth as big
E) The flux stays the same
3. Electric charges produce electric fields. What else can also produce electric fields?
A) Constant electrical currents
B) Moving magnetic charges
C) Constant magnetic fields
D) Changing magnetic flux
E) Moving neutral conductors
4. Which of the following describes the type of current that is produced in a commercial
generator and experienced when you plug something into an outlet
A) The potential difference is constant and always has the same sign
B) The potential difference is always the same sign, but varies widely in magnitude,
though it is never zero
C) The potential difference is always the same sign, though it can also be zero, but it
never reverses
D) The potential difference is always the same magnitude, but it switches from
positive to negative and back again many times a second
E) The potential difference changes in both magnitude and sign, varying smoothly
from a maximum (positive) to minimum (negative), and back again
5. In an ideal (infinitely long, closely spaced wire loops) solenoid, how does the
magnetic field inside the solenoid compare to the magnetic field outside the solenoid?
A) It is the same magnitude and points in the same direction
B) It is the same magnitude but points in the opposite direction
C) It is zero outside the solenoid, but not zero inside
D) It is zero inside the solenoid, but not zero outside
E) None of the above are correct
6. If two long, parallel wires have current flowing through them in opposite directions,
the wires will
A) Attract each other
B) Repel each other
C) Cause each wire to feel a stretching force, trying to make it longer
D) Cause each wire to have a compression force, trying to make it shorter
E) Parallel wires have no force on each other.
7. A loop of wire in a constant magnetic field carrying a current I can feel what kind of
forces?
A) Torque, but no net force
B) Net force, but no torque
C) Net force or torque
D) Neither net force nor torque
E) Compression forces, but not expansion forces
8. A ground fault circuit interrupter (GFCI or GFI) cuts off the current to an outlet
whenever
A) There is more than a specified amount of current flowing through the live wire
B) There is more than a specified amount of current flowing through the neutral wire
C) The current going back through the neutral wire doesn’t match the current
flowing out through the live wire
D) There is too little current flowing through the neutral wire
E) There is too little current flowing through the live wire
9. Calculate the integral
v∫ B ⋅ ds for the dashed loop sketched below.
Several current
values flowing through the plane of the paper are drawn in.
A) + ( 2 A ) μ0
6A
B) + ( 4 A ) μ0
3A
2A
C) − ( 2 A ) μ0
1A
D) − ( 4 A ) μ0
E) None of the above
10. Between the plates of a parallel plate capacitor that is being charged up, will there be
a magnetic field? Why or why not?
A) Yes, because actual electrical current is flowing between the two plates
B) Yes, because the changing electric field acts as a “displacement current” that
produces magnetic fields
C) Yes, but only if there is a dielectric material in between with magnetic properties
D) No, because there is no current actually flowing in this region
E) No, because the actual current flowing is cancelled by the displacement current
Part II: Short answer [20 points]
Choose two of the following questions and give a short answer (1-3 sentences) or
brief sketch (10 points each).
11. The capacitor at right contains charge Q in it. Explain qualitatively
what happens when you close the switch. Use equations if you wish.
12. Compare and contrast Gauss’s Law for electric and magnetic fields. What is
fundamentally different about magnetic fields that makes the rule different?
13 Explain qualitatively the Hall effect. It is not necessary to use any equations.
Part III: Calculation: [60 points]
Choose three of the following four questions and perform the indicated
calculations (20 points each)
8Ω
4Ω
14. Sketched at right is part of a circuit. Not shown is the rest of the circuit, which has 3
A flowing in along the top wire, and 3 A flowing out along the bottom wire. Call the
currents I1 and I2 the two currents flowing in each of the
3A
resistors, in the presumptive directions sketched.
(a) Use Kirchoff’s first law to derive a relationship
between the currents
I2
(b) Use Kirchoff’s second law to write a second
I1
expression relating the two currents
+
(c) Solve for the two currents I1 and I2. Did we orient the
3 A – 12 V
two currents correctly; that is, is the actual current in
the directions chosen, or have we chosen them
incorrectly?
(d) We wish to check that the current I2 flowing through the 8 Ω resistor was
calculated correctly. Redraw the partial circuit diagram, adding an ammeter and
voltmeter to check the voltage and current across the 8 Ω resistor. What current
and voltage should be registered across this resistor?
26.2 cm
15. Pions come in three types, π0 with charge zero, and π± with charge ± e. A pion
enters a region with constant magnetic field B = 0.600 T pointing out of the plane of
the paper, passes through a velocity selector, and then into a region with just the
constant magnetic field.
(a) The velocity selector is designed to accept only pions with
velocity v = 5.00 × 107 m/s to the right. What is the
magnitude and direction of the electric field E required in the
velocity selector to make sure this works?
(b) After passing through the velocity selector, the pion curves in
a graceful arc and hits the wall as sketched a distance 26.2 cm
away from where it entered. What is the mass of the
pion?
B
(c) Was the particle a π0, a π+, or a π-?
π
Electric and
Magnetic fields
Magnetic
fields only
16. A certain cable consists of three parallel conductors, one a
C
very slender wire perpendicular to this page, the second a
B
coaxial cylinder of radius 2 cm, and the third another
coaxial cylinder of radius 4 cm. The wire at the center is
carrying a total current of 1 A flowing directly out of the
A
paper. The first cylinder has 7 A flowing directly into the
paper. The outer cylinder may carry additional current in
either direction. At right is sketched an end-on view of the
cable.
(a) The magnetic field at point A, 1 cm from the axis of the
4 cm
2 cm
cylinder, is measured. What is its magnitude and
direction?
(b) The magnetic field at point B, 3 cm from the axis of the cylinder, is measured.
What is its magnitude and direction?
(c) At point C, 5 cm from the axis, it is found that there is no magnetic field. What is
the total current and its direction in the outer cylinder?
B = 4000t 2 − 30t
where t is the time in seconds and B is the magnetic field in tesla.
6 cm
(a) Find the total magnetic flux through the loop as a function of
t.
(b) At time t = 0.0100 s, the voltage across the two external wires is measured. What
is the voltage difference?
(c) In part (b), which wire is the positive wire?
6 cm
17. A coil of wire is in the shape of a right triangle with both legs having size s = 6
cm and consisting of 500 turns of wire. It lies in a region where the magnetic
field in the direction out of the plane is changing according to the formula