Name _________________
Test 2
March 4, 2015
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. In the Hall effect, a wire is placed in a magnetic field. An electric potential is
generated that is __________ to the direction of current flow and _________ to the
magnetic field.
A) Perpendicular, perpendicular
B) Perpendicular, parallel
C) Parallel, perpendicular
D) Parallel, parallel
E) None of the above
2. Which of the following units is equivalent to an ohm ()?
A) V/A
B) A/V
C) A·V
D) W/A
E) W/V
3. The cross product of the unit vectors ˆi  kˆ is
B) iˆ
C) ĵ
D) jˆ
E) k̂
A) î
4. The loop at right contains currents as marked. What is the equation
derived from Kirchoff’s second law for this loop?
+
–
5
3
7
I2
I1
A)
B)
C)
D)
E)
5 + 3I1 + 7I2 = 0
5 – 3I1 + 7I2 = 0
5 + 3I1 – 7I2 = 0
5 – 3I1 – 7I2 = 0
None of the above
5. If 10 A of current is running through a wire for 20 s, how much total charge passes
through?
A) 1/200 C B) ½ C
C) 1 C
D) 2 C
E) 200 C
I1
I2
6. Three currents are joined at a point as sketched at right. What is
the equation derived from Kirchoff’s first law from this vertex?
I3
A) I1 + I2 = I3 B) I1 + I3 = I2 C) I2 + I3 = I1 D) I1 + I2 + I3 = 0 E) None of these
7. When a capacitor is discharged through a resistor, the capacitor initially has energy in
it, but at the end it does not. Where does the energy go?
A) It is stored as electric energy in the resistor
B) It is stored as electric energy in the wires
C) It is converted to heat in the capacitor
D) It is converted to heat in the wires
E) It is converted to heat in the resistor
8. The formula for the magnetic field given for a long solenoid, B  0 NI L , is
A) Correct everywhere
B) Correct inside the solenoid; outside it is approximately zero
C) Correct outside the solenoid; inside it is approximately zero
D) Correct only at the exact center of the solenoid
E) Correct only on the surface of the solenoid
9. Qualitatively, two parallel wires with current running through them feel a force
because
A) Current from one creates a magnetic field, which the other feels
B) Current from one creates an electric field, which the other feels
C) The Hall effect causes charges to accumulate on one side of each of the wires,
which then attract each other
D) One wire creates an electric potential which the other one feels
E) None of the above
10. Which of the following is a correct relation for the current density J in terms of the
current I, the cross sectional area A, and the length L?
A) J = IL B) J = I/L C) J = I/A D) J = IA E) J = I/(LA)
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. A light bulb is essentially a resistor. Explain qualitatively how a light bulb works. It
turns out that the resistance of a light bulb that is sitting on a shelf is rather different
from the resistance of a light bulb in operation. Explain why, giving one relevant
formula.
12. A student is trying to measure the current and the
voltage for the resistor at right. Sketch where an
ammeter and a voltmeter should be added to
make this work. You may draw them directly on
the diagram provided, if you wish
–
+

R
C
13. Define magnetic flux, giving any relevant formula. Then give a simple way to
compute the total magnetic flux out of an enclosed region.
Part III: Calculation: [60 points]
`
Choose three of the following four questions and perform the indicated
calculations (20 points each)
14. A gallon of gasoline can produce approximately 1.20  108 J of energy. Suppose an
electric car has a battery with the equivalent of five gallons of gasoline, or 6.00  108
J.
(a) Suppose it is being charged by a 500 V source that is pumping 16.0 A into the car
(larger voltages or currents can be dangerous). How many hours will it take to
recharge the car?
(b) You don’t want the cables to consume too much power. If the cables charging the
car (and therefore carrying the current) are consuming 320 W of power, what
must their resistance be?
(c) Assume the cables are made of copper (   1.68 108   m ), have a circular
cross-section, and have a total length of l  25.0 m . What is the radius r of
cable required to obtain the resistance found in part (b)?
15.0 k
10.0 V 25.0 F
– +
10.0 k
15. A 10.0 V battery is going to charge a 25.0 F capacitor
through the combination of resistors as sketched at right
(a) What is the equivalent resistance of the three resistors?
14.0 k
(b) What is the time constant  for this charging process?
(c) The switch is closed at t = 0. At what time t will there be 225 C of charge on
the capacitor?
16. A certain mass spectrometer contains a magnetic field of magnitude B = 0.124 T.
Then Na+ ions with charge q = + 1.60210-19 C are injected. The velocity selector
only allows ions with a velocity of v = 8.64104 m/s to pass through. After
passing through the straight section, the sodium ions curve, as sketched.
(a) What direction is the magnetic field pointing?
(b) What magnitude of electric field is required in the straight section to let only this
velocity through? What direction is the electric field pointing?
(c) A typical Na+ ion has a mass of 3.8210-26 kg. Find the radius in the curved
portion of its track.
17. A long tri-coaxial cable has a thin center wire (current 1.00 A out) surrounded by a
thin cylindrical layer with radius r = 2.00 mm (current
1 A out
5.00 A in), surrounded by another thin cylindrical layer
with radius r = 4.00 mm (current 4.00 A out). Calculate
4 mm
the magnitude of the magnetic field, as well as its
5 A in
direction (where appropriate) at an arbitrary point the
2 mm
following distances from the center:
(a) r = 1.00 mm
(b) r = 3.00 mm
4 A out
(c) r = 5.00 mm