Physics 6B – Summer 2007 Final
Question 1
An electron passes through two rectangular regions that contain uniform magnetic fields,
B1 and B2. The field B1 is stronger than the field B2. Each field fills the region completely.
How does the speed v1 of the electron in region 1 compare with the speed v2 in region 2?
B
B
B
B
A. The speeds are the same in both
regions.
B. The speed v1 is greater than v2,
because B1 is stronger than B1.
C. The speed v1 is less than v2, because
the radius of the circular path in
region 1 is less than that in region 2.
D. The speed v1 is less than v2, because
the electron accelerates as it goes
from region 1 to region 2.
E. The speed v1 is less than v2, because
B1 is stronger than B2.
B
B
B
B
The correct answer is A because magnetic forces are always at right angles to the
velocity. Such forces can change the direction of the velocity vector, but not its
magnitude (speed).
Question 2
Three particles are moving perpendicular to a uniform magnetic field and travel on
circular paths (see the drawing). They have the same mass and speed. List the particles in
order of their charge magnitude, largest to smallest.
A.
B.
C.
D.
E.
3, 2, 1
3, 1, 2
2, 3, 1
1, 3, 2
1, 2, 3
If the mass and speed are the same, the magnetic force only depends on charge. The
greater the magnitude of the charge, the greater the magnitude of the force, an the more
the particle will bend. Therefore the correct answer is E.
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Question 3
Suppose you want to produce a strong magnetic field that is constant in magnitude and
direction in a region of space. Which one of the following would you choose to produce
this field?
A. The interior region of a long current-carrying solenoid.
B. The exterior region of a long current-carrying solenoid.
C. The region surrounding a long, straight, current-carrying wire
D. The region surrounding a loop of a current-carrying wire.
The only configuration that gives an (approximately) constant B-field is A.
Question 4
Three long, straight wires are carrying currents that have the same magnitude. In C the
current is opposite to that in A and B. The wires are equally spaced. Each wire
experiences a net force due to the other two wires. Which wire experiences a net force
that has the greatest magnitude?
A. A
B. B
C. C
D. All three wires feel the same force
On wire B the forces due to A and C act in the same direction and so reinforce each other.
On the other hand, on wires A and C the forces (due to B and C and A and B
respectively) act in opposite directions and therefore tend to cancel out. Correct answer
is B.
Question 5
The drawing shows four situations in which two very long wires are carrying the
samecurrent, although the direction of the currents may be different. The point P in the
drawings is equidistant from each wire. Which one (or more) of these situations gives rise
to a zero net magnetic field at P?
A. 2 and 4
B. Only 1
C. Only 2
D. 2 and 3
E. 3 and 4
1: the two fields add (both into the paper)
2: the two fields cancel (one into the paper, one out of the paper)
3: field from vertical wire into the paper, field from horizontal wire also into the paper
4: field from vertical wire out of the paper, field from horizontal wire into the paper
Æ correct answer is A
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Question 6
Two different charges, q1 and q2, are placed at two different locations, one charge at each
location. The locations have the same electric potential V. Do the charges have the same
electric potential energy?
A. Yes. If the electric potentials at the two locations are the same, the electric
potential energies are also the same, regardless of the type (+ or -) and magnitude
of the charges placed at these locations.
B. Yes, because electric potential and electric potential energy are just different
names for the same concept.
C. No, because the electric potential V at a given location depends on the charge
placed at that location, whereas the electric potential energy does not.
D. No, because the electric potential energy at a given location depends on the
charge placed at that location as well as the electric potential V.
U1=q1V and U2=q2V Æ correct answer is D
Question 7
A proton is released from rest at point A in a constant electric field and accelerates to
point B (see part a of the drawing). An electron is released from rest at point B and
accelerates to point A (see part b of the drawing). The distances traveled by the proton
and the electron are the same. How does the change in the proton's electric potential
energy compare with the change in the electron's electric potential energy?
A. The change in the proton's electric potential energy is the same as the change in
the electron's electric potential energy.
B. The proton experiences a greater change in electric potential energy, since it has a
greater charge magnitude.
C. The proton experiences a smaller change in electric potential energy, since it has a
smaller charge magnitude.
D. The proton experiences a smaller change in electric potential energy, since it has a
smaller speed at B than the electron has at A. This is due to the larger mass of the
proton.
E. One cannot compare the change in potential energies because the proton and
electron move in opposite directions.
For proton, charge +e:
For electron, charge –e::
Æ correct answer is A
ΔU = UB – UA = (+e)VB - (+e) VA = e(VB - VA )
ΔU = UA – UB = (-e)VA - (-e) VB = e(VB - VA )
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Question 8
Two identical resistors are connected first in series and second in parallel. The equivalent
resistances of the two types of connections are, respectively, RS and RP. What is the ratio
RS/RP?
A. ¼
B. 4
C. ½
D. 1
E. 2
RS = 2R while RP=½R Æ correct answer is B
Question 9
The following four equations are supposed to result from applying Kirchhoff's rule to the
circuit shown in the drawing. However, one of the equations is written incorrectly. Which
one is it?
A. I1 = I4 + I5
B. I3 = I1 + I2
C. I6 = I3 + I5
D. I2 = I4 + I6
Kirchoff at node A: I4 + I5 = I1
Kirchoff at node B: I1 + I3 = I2
Kirchoff at node C: I3 + I5 = I6
Kirchoff at node D: I4 + I6 = I2
Æ correct answer is B
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Question 10
The drawings show a number of different possibilities for connecting an ammeter (AM)
and a voltmeter (VM) to a circuit, in order to measure the current in and the voltage
across the resistor labeled R2. Which one of the possibilities shows the correct
connections?
A.
D.:
B.
C.
E.
Correct answer is A because VM must be placed in parallel with R2 and AM must be
placed in series with R2.
Question 11
Three capacitors are identical, each having a capacitance C. Two of them are connected
in series. Then, this series combination is connected in parallel with the third capacitor.
What is the equivalent capacitance of the entire connection?
A. ½ C
B. 1/3 C
C. 3 C
D. 2/3 C
E. 3/2 C
The series combination has capacitance Ceff = ½C. Then we have Ceff in parallel with C,
for a total capacitance Ceff = C = ½C + C = 3/2 C Æ correct answer is E
Question 12
A magnetic field is perpendicular to the plane of a flat coil. Since the magnitude of the
field is increasing, an emf will be induced in the coil unless something is done to prevent
it. Except for one option, all of the following are possible options that could be used to
keep the emf at the zero level. Which option could not be used?
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A. Decrease the area of the coil.
B. Increase the angle between the field and the normal to the plane of the coil.
C. Simultaneously decrease the area of the coil and increase the angle between the
field and the normal to the plane of the coil.
D. Reduce the time interval during which the magnitude of the field increases.
D does not work because emf = Δφ/Δt Æ correct answer is D
Question 13
A long, vertical, straight wire carries a current I. The wire is perpendicular to the plane of
a circular metal loop and passes through the center of the loop (see the drawing). The
loop is allowed to fall and maintains its orientation with respect to the straight wire while
doing so. In what direction does the current induced in the loop flow?
A. There is no induced current.
B. Around the loop from A to B to C to A
C. Around the loop from C to B to A to C
As the loop falls, the flux does not change Æ no induced current Æ correct answer is A
Question 14
The drawing shows a top view of two circular coils of conducting wire lying on a flat
surface. The centers of the coils coincide. In the larger coil there is a switch and a battery.
The smaller coil contains no switch and no battery. Describe the induced current that
appears in the smaller coil when the switch in the larger coil is closed.
A. It flows counterclockwise forever after the
switch is closed.
B. It flows clockwise forever after the switch is
closed.
C. It flows counterclockwise, but only for a short
period just after the switch is closed.
D. It flows clockwise, but only for a short period
just after the switch is closed.
Current in large coil flows counterclockwise Æ by Lenz’s law current in small coil must
flow anticlockwise. But only for a small time, because once the current in the outer coil
becomes constant, the emf in the smaller coil goes away Æ correct answer is D
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Question 15
A point charge q is located at the origin. A charge q0 can be placed at a point P1, which is
a distance r from the origin (top drawing). Or, a charge 2q0 can be placed at P2, which is
a distance 2r from the origin (bottom drawing). All charges are positive. Which statement
is true about the electric potentials at P1 and P2?
A. The electric potential at P1 is less than that at P2,
because q0 is smaller than 2q0.
B. The electric potential at P1 is less than that at P2,
because r is smaller than 2r.
C. The electric potential at P1 is greater than that at P2,
because r is smaller than 2r.
D. The electric potential at P1 is the same as that at P2.
V(P1)=kq/r and V(P2)=kq/(2r) Æ correct answer is C
Question 16
Five volts is applied to two 2 ohm resistors in series. The resulting current is
A. 5A
B. 2.5 A
C. 1.25 A
D. 0.8 A
E. 0.4 A
Req = 2R = 4Ω. I=V/Req = (5/4) A = 1.25 A Æ correct answer is C
Question 17
What is the charge on the 30μF capacitor in the Figure?
A.
B.
C.
D.
40 C
0.00054 C
1389 C
0.00018 C
The voltage across C3 is V=18V Æ Q=CV=30 10-6 18 C = 0.00054 C Æ correct answer
is B
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Question 18
Mutual induction leads to an induced emf εs in a secondary coil when a change ΔIP in the
current in the primary coil occurs in a time Δt. The mutual inductance between the coils
is M. The relative positions of the coils is then changed, after which a change of 2 ΔIP in
the primary current in a time of ½ Δt is needed to produce the same induced emf εs in the
secondary coil. What is the mutual inductance with the coils in their new positions?
A. ¼ M
B. ½ M
C. M
D. 2 M
E. 4 M
ε = Μ ΔI/Δt and ε = Μnew (2ΔI)/(½ Δt) = 4 Μnew ΔI/Δt Æ Μnew = ¼ M Æ correct
answer is A
Question 19
Inductor 1 stores the same amount of energy as inductor 2, although its inductance is only
half the inductance of inductor 2. What is the ratio I1/I2 of the currents in the two
inductors?
A. 2.00
B. 1.41
C. 4.00
D. 0.50
E. 0.25
U = ½ L1I12 and U = ½ (2L1) I22 Æ I12 = 2 I22 Æ I1 / I2 = 1.41 Æ correct answer is B
Question 20
Lines of magnetic field are
A. Always straight lines
B. Terminate on negative charges
C. Point in the direction of the magnetic force exerted on a positive charge
D. Are always perpendicular to the equipotentials
E. Point in the direction of the magnetic field
Correct answer is E
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Question 21
In an ionic solution, positive sodium ions (Na+) are moving to the right and negative
chlorine ions (Cl-) are moving to the left. In which direction is the current due to the
motion of (i) the sodium ions and (ii) the chlorine ions
A. Both to the right.
B. Current due to Na+ is to the right; current due to Cl- is to the left.
C. Current due to Na+ is to the left; current due to Cl- is to the right.
D. Both to the left.
By convention current flows in the direction of motopn of positive charges and in the
direction opposite to the motopn of negative charges Æ correct answer is A
Question 22
The potential difference Vab=Va-Vb is
A.
B.
C.
D.
E.
+3.33V
+3V
-3V
-2.67V
-3.33V
a
b
Equivalent resistance of the three resistors on the left: 1/RL = 1/10+1/20+1/10 gives
RL=4Ω.
Equivalent resistance of the three resistors on the right: 1/RR = 1/20+1/10+1/20 gives
RR=5Ω.
Equivalent resistance of the 6 resistors R=RL+RR=9Ω.
Current through the circuit is I=ε/R=6V/9Ω=2/3A. This current is flowing
counterclockwise.
Vba=Vb-Va = IRL = (2/3) 4 V = + 8/3 V = 2.67 V
Vab= -Vba= - 2.67 V Æ correct answer is D
Question 23
An electric current is induced in a conducting loop by all but one of these processes.
Which one does not produce an induced current?
A. Rotating the loop so that it cuts across magnetic field lines
B. Placing the loop so that its area is at 45o to a changing magnetic field
C. Moving the loop parallel to uniform magnetic field lines
D. Expanding the area of the loop while it is perpendicular to a uniform magnetic
field
Correct answer is C because the flux is not changed in this case.
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Question 24
A capacitor and a resistor are connected through a switch to an emf. Before the switch is
closed, the capacitor is uncharged. At the instant after the switch is closed
A.
B.
C.
D.
E.
The current in the circuit is zero
The voltage across the capacitor is ε
The voltage across the resistor is zero
The voltage across the resistor is ε
Both A and C are true
Kirchoff’s law for voltage: ε = IR + Q/C. But at time t=0, Q=0, thus ε = IR
Æ correct answer is D
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