True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 96.
The exam period was 90 minutes; the mean was 72.1; the median was 74.
Click here to see page1
page2 of the formula sheet that came
with the exam.
Four infinite wires carry currents parallel to the z-axis as
shown in the figure. Each wire is spaced from the z-axis by
a meters. The magnitude of the current in each of the wires is
equal to I0. Two of the wires carry current in the
positive z-direction and two of the wires carry current in the
What is the magnetic field B(0) at the origin?
(Hint: Use the principle of superposition and the right hand rule to
solve this. Keep track of the contribution from each wire.)
(a) The magnetic field everywhere stays the same.
(b) The magnetic field everywhere is one half what it was before.
(c) The magnetic field at the origin goes to zero.
An infinite coaxial cable consists of a solid center conductor of
radius 0.01 meter, and an outer conducting cylindrical shell of radius
0.1 meter. A small section of the cable is shown in the figure. A
current of 4 amperes flows to the right uniformly distributed in the
center conductor and a current of 2 amperes flows to the left uniformly
distributed on the outer conductor. The center of the coaxial cable is
the axis of cylindrical symmetry.
What is the magnitude of the magnetic field 0.8 meter from the axis of
(a) 2.0 × 10-7 tesla
(b) 5.0 × 10-7 tesla
(c) 8.0 × 10-7 tesla
(d) 1.0 × 10-6 tesla
(e) 1.5 × 10-6 tesla
Between time t = 0 and t = τ the magnetic
field in the region of space pertaining to this problem is given by
B0 is a positive number. At earlier times the field
is constant and is given by B(t) =
B0z and at later times the field is
zero. This means that the magnetic field at time t = 0 points in
the positive z-direction and has a magnitude of
B0 and then it linearly decreases in magnitude
reaching zero at time t = τ. This is shown on the
graph below. A conducting loop of area A that incorporates a
resistor with a resistance R0 lies in the
x-y plane as shown in the adjacent figure.
Which one of these statements regarding the current in the loop
during the time interval between t = 0 and t =
τ is true?
(a) Since there is no battery, there is no current.
(b) There is a current that flows counter-clockwise as viewed from above.
(c) There is a current that flows clockwise as viewed from above.
(a) ε = 2τR0 / B0
(b) ε = AB0 / τ
(c) ε = AτB0
(d) ε = τB0 / R0
(e) ε = AR0B0 / 2τ
Two batteries are arranged in a circuit with two resistors as shown
in the figure. The resistance of each resistor is not given, but the
indicated currents are observed to flow through the two resistors.
(Hint: Redraw the circuit to see explicitly what circuit elements are
in series and which are in parallel. Pay attention to the polarity of
the batteries in the figure.)
Which battery supplies the most power to the resistors?
(a) the 20 V battery
(b) the 30 V battery
(a) 12.5 Ω
(b) 10 Ω
(c) 5 Ω
(d) 4 Ω
(e) 2 Ω
A circuit consists of a capacitor, two 10 Ω resistors, and a
100 V battery connected as shown in the figure. The switch is closed
(connected) at time t = 0. Assume that the capacitor is uncharged
before the switch is closed.
It is observed that the charge stored on the capacitor as a function of
time while it charging is given by
Find the capacitance C of the capacitor
(a) 1.0 × 10-8 farads
(b) 5.0 × 10-8 farads
(c) 1.0 × 10-7 farads
(d) 2.0 × 10-7 farads
(e) 1.0 × 10-6 farads
(a) At t = 0 the same current flows through the two
(b) At t = ∞ the same current flows through the two
(c) At t = 0 twice the current flows through one resistor compared to
A circuit is constructed out of a 0.01 F capacitor, four resistors,
and a 30 V battery connected as shown in the figure. The switch is
closed (connected) at time t = 0. Assume that the capacitor is
uncharged before the switch is connected.
At t = 0 the current flowing though the battery is:
(a) 2.06 A
(b) 1.08 A
(c) 2.54 A
(a) 1.125 J
(b) 1.000 J
(c) 0.750 J
(d) 0.125 J
(e) 0.050 J
(a) The stored energy in the capacitor with 20 Ω resistors
is larger than the stored energy with 15 Ω resistors.
(b) The stored energy in the capacitor with 20 Ω resistors is
smaller than the stored energy with 15 Ω resistors.
(c) The stored energy in the capacitor with 20 Ω resistors is equal
to the stored energy with 15 Ω resistors.
A neutral, conducting rod of length L = 0.4 m is moving with
constant speed v = 2 m/s in the positive x direction in
the presence of a magnetic field B = 0.35 T directed into
the page as shown.
The bottom end of the rod has
(a) excess + charge.
(b) excess - charge.
(a) 0.7 V/m
(b) 0.28 V/m
(c) 1.75 V/m
A single circular loop of wire of radius R = 0.24 m carries
current I = 0.4 A, and is oriented as shown in the diagram. A
constant magnetic field points along the negative y-direction
having magnitude B = 0.7 T. To begin with, the loop is fixed in
In the diagram at the right, the two arrows labeled "a)" and "b)"
denote two possible directions for the magnetic moment of the loop.
Which is actually the correct direction?
(a) Orientation "a)" is correct for the magnetic moment.
(b) Orientation "b)" is correct for the magnetic moment.
(a) 0.025 N⋅m
(b) 0.044 N⋅m
(c) 0.066 N⋅m
(d) 0.21 N⋅m
(e) 0.37 N⋅m
Two charged particles enter a region of constant and uniform magnetic
field directed out of the page (positive z direction) through a
small opening traveling along the positive y-axis. The path
taken by the two particles is shown in the diagram. Both particles
enter the region of magnetic field with the same speed and both have the
same magnitude charge.
What type of charge are the two particles?
(a) Particle #1 is + and particle #2 is -.
(b) Particle #1 is - and particle #2 is +.
(a) 0.186 m
(b) 0.215 m
(c) 0.372 m
(d) 0.487 m
(e) 0.669 m
(a) 9.6 × 10-16 V/m directed toward the bottom of the page
(b) 6.0 × 103 V/m directed toward the bottom of the page
(c) 9.6 × 10-16 V/m directed toward the top of the page
(d) 6.0 × 103 V/m directed toward the top of the page
(e) 9.6 × 10-16 V/m directed out of the page.
(a) Situation 1
(b) Situation 2
(c) Situation 3
(d) Situations 2 and 3
(e) Situations 1, 2 and 3