Name _________________
Test 2
March 5, 2014
This test consists of three parts. Please note that in parts II and III, you can skip one
question of those offered.
Solenoid
Loops
Force
0 NI
τ  IA  B
Between
B
Possibly useful formulas:
U   IA  B
Wires
L
Cyclotron
Constants
0 I1 I 2
F
Motion

19
e  1.602 10 C
Field from Straight Wire
L
2 d
mv  qRB
7
0  4 10 T  m/A
I
qB
B  0  cos 1  cos  2 

Hall Effect
4 a
m
Resistance
IB
0 I

V


B
H
  0 1   T  T0  
tnq
RC Circuits
2 a
t 
Q  Q0 e
R  R0 1   T  T0  
Biot-Savart
Ampere’s Law
Q  C 1  e t  
L
0 I ds  rˆ
R
B
A
 B  ds  0 I
  RC
4  r 2
Circles
C  2 R
A   R2
Triangles
A  12 BH
Spheres
A  4 R 2
V  43  R 3
Cylinders
V   R2 L
Alat  2 RL
Metric Prefixes
k = 103  = 10–6
c = 10–2 n = 10–9
m = 10–3 p = 10 –12
Part I: Multiple Choice [20 points]
For each question, choose the best answer (2 points each)
1. A loop of current in a constant magnetic field has the largest energy when its area
vector is ________ to the field and the smallest energy when it is _________ to the
field
A) Parallel, anti-parallel (opposite the field)
B) Anti-parallel (opposite the field), parallel
C) Parallel, perpendicular
D) Perpendicular, parallel
E) Anti-parallel (opposite the field), parallel
2. The formula given for the magnetic field for an ideal solenoid is
A) Correct both inside and outside, and the field points the same way both places
B) Correct both inside and outside, but the field points opposite directions
C) Correct only inside the solenoid; outside the field is approximately zero
D) Correct only outside the solenoid; inside the field is approximately zero
E) None of the above
3. Which of the following explains how
a motor works?
A) Electric fields cause forces on
stationary charges in the wires
B) Electric fields cause forces on
currents in the wires
C) Magnetic fields cause forces on
stationary charges in the wires
D) Magnetic fields cause forces on
currents in the wires
E) Magic fairies named Maxwell,
Ampere, Biot, and Savart push
them around
4. If two current-carrying wires are
parallel and near each other, will
there be a force between them?
A) Yes: attractive if the currents run
opposite, repulsive if the currents
run the same way
B) Yes: attractive if the currents run
the same way, repulsive if the
currents run opposite
C) Yes: always attractive
D) Yes: always repulsive
E) No
5. In a velocity selector, there are charged particles in a region of a magnetic field. How
come the particles move in a straight line, despite the magnetic field?
A) The particles are moving parallel to the magnetic field, so no force
B) The particles are moving anti-parallel to the magnetic field, so no force
C) The particles move so slowly that the magnetic force is negligible
D) The particles attract electrons that cancel the charge, so no force
E) There is an electric field that exactly balances the magnetic field
R1
6. For the two resistors at right, what is the formula for the total resistance?
1
1
1
1 1
1
A) R  R1  R2 B)  R1  R2 C) R  
D)
 
E) R  R1 R2
R1 R2
R R1 R2
R
7. If a light bulb is consuming 60 W of power from a 120 V source, what is the current
in the light bulb?
A) 7200 A
B) 2A
C) ½ A
D) 1/30 A
E) 1/7200 A
R2
8. In the formula F  IL  B for the force
on a wire in a magnetic field, what
direction is the vector L supposed to
point?
A) Along the wire in the direction the
current is flowing
B) In the direction of the magnetic field
C) Opposite the direction of the
magnetic field (anti-parallel)
D) Perpendicular to both the wire and
the magnetic field
E) Circling the wire in a manner
corresponding to the right-hand rule
9. What happens to a charged particle in a
uniform magnetic field, if it is initially
moving perpendicular to the magnetic
field?
A) It oscillates back and forth like a
simple harmonic oscillator
B) It moves in a circle perpendicular to
the magnetic field
B) It moves in a straight line at constant
speed
C) It moves in a straight line but at
constant acceleration
D) It switches its direction to move along the magnetic field
E) It gradually slows down and stops
10. Suppose the magnetic field is integrated over the surface of a sphere, and the result is
positive,  B  ndA  0 . What does this tell us about what is going on inside the
sphere?
A) There is net positive charge inside the sphere
B) There must be the north end of a magnet or solenoid inside
C) There must be the south end of a magnet or solenoid inside
D) There is a net current flowing into the region
E) This should be impossible; this integral must always be zero
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. In the circuit sketched at right, there is initially no charge on the
capacitor. Explain qualitatively what happens when you close the
circuit, giving any relevant equations.
–
+

R
C
12. Explain qualitatively what the Hall effect is. You do not need any equations, though
a sketch might help.
13. Explain how an ideal battery differs from a realistic battery. A circuit picture
explaining this might help.
14. Consider the circuit at right. Assume for the moment that the
currents are as marked; that is to say, the top two branches
have current to the right, and the bottom one to the left.
(a) Use Kirchoff’s first law to get one or more simple
relationships between the three currents.
–
+
I1
6V
12 V
– +
3
Part III: Calculation: [60 points]
`
Choose three of the following four questions and perform
the indicated calculations (20 points each)
I2
I3
8
(b) Use Kirchoff’s second law to get one or more additional relationships between all
three currents.
(c) Find all three currents I1, I2, and I3. Which direction (right or left) are the three
currents actually moving?
180 V
– +
15. Two resistors are powered by a 180. V power source as shown at
right, and the current is measured by the ammeter A. Resistor R1 is
made of carbon, and at T0  20C , has resistance R1  20.0 k and
has temperature coefficient of resistivity 1  5.0 104 / C .
Resistor R2 has unknown resistance and is made of an unknown
substance.
(a) At T0  20C , the ammeter reads I  4.00 mA . What is the
resistance of the second resistor R2 at this temperature?
A
R1
R2
(b) The entire structure is now immersed in boiling water at temperature T  100C .
It is discovered that the ammeter still reads I  4.00 mA . What is the
temperature coefficient of resistivity  2 for the second resistor?
16. A loop of wire is in the shape of an equilateral triangle of
side 6.00 cm, with a current of 3.00 A traveling clockwise
around the wire. We are interested in the magnetic field at
the exact center of the triangle.
(a) What is the angle  in the diagram at right? What is
the distance d from one of the sides of the triangle to
the center?

d
6.00 cm
(b) What is the magnetic field (magnitude and direction) at the center of the triangle
due to the loop?
(c) A positron (mass m  9.109 1031 kg , charge e  1.602 1019 C ) is at the
center of this triangle, moving to the right at v  1.27 107 m/s . Find the
acceleration (direction and magnitude) of this positron.
17. A coaxial cable has a thin center wire surrounded by a thin
cylindrical layer with radius r = 3.00 mm. The central wire
(small dot) has a current of I1 = 1.20 A coming out of the paper
towards us, and the cylindrical layer (solid circle) has an
unknown current I2 in it.
(a) Find the magnetic field at a distance r = 2.00 mm from the
central wire. Find its magnitude, and describe or sketch its
direction.
I2
I1 out
5 mm
3 mm
(b) At a distance of r = 5.00 mm, the magnetic field is found to have a magnitude of
12.00 T, oriented in a clockwise direction around the cable, as shown by the
dashed curves. What is the current I2, and is it into or out of the paper?
12 T