Download Practice Final Exam (MC) w/ Answers

Final
On the Scantron form, be sure to indicate your "Test Form" (i.e., A, B, C, or D) and your Code Number (i.e.,
labeled the "Exam Number" on the Scantron form). The "Test Form" is indicated at the bottom of this page.
This exam contains 34 problems. All problems count equally.
If no answer is completely correct, choose the answer that is closest.
k = 1/4πεo = 9.0 x 109 Nm2/C2
µ0/4π = 1.0 x 10-7 N/A2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Two particles have charges Q and − Q (equal magnitude and opposite sign) are separated by a
distance d. For a net force of zero to be exerted on a third charge it must be placed:
A) midway between them
B) on the line joining them to the side of Q opposite - Q
C) on the line joining them to the side of - Q opposite Q
D) at none of these. There is no place that works.
2) This problem relates to Fig. 1 on the Figures Page. Two charges of strength 2 µC and 5 µC are
located 1 m from the origin on the x and y axes respectively. The force (in N) on a charge of
strength 10 µC, located at the origin, is:
A) - 0.45 ^
i - 0.18 ^
j
B) + 3.0 ^
i + 9.0 ^
j
C) - 0.18 ^
i - 0.45 ^
j
D) - 1.8 ^
i + 3.6 ^
j
3) This problem also relates to Fig. 1 on the Figures Page. Assuming that the charges are brought in
from infinity, the work (in J) required to establish this configuration is approximately:
A) 0.69
B) 0.28
C) 0.92
D) 0.13
4) Charge is distributed on the surface of a spherical conducting shell. A point particle with charge q
is placed somewhere inside. The electrical force on the particle is smallest when it is:
A) inside and near the surface
C) anywhere inside - the force is the same.
B) at the center
D) anywhere inside - the force is zero.
5) The work required to bring charge Q from infinity to form a shell of radius R is:
A) kQ/R
B) kQ2/R
C) kQ2/2R
1
D) kQ/2R
6) When the dipole moment of a dipole in a uniform electric field rotates to become more nearly
aligned with the field, the field does:
A) positive work and the potential energy increases
B) negative work and the potential energy increases
C) positive work and the potential energy decreases
D) no work
7) Choose the INCORRECT statement:
A) According to Gauss’s law, if a closed surface encloses no charge, then the electric field must
vanish everywhere on the surface
B) Gauss’s law can be derived from Coulomb’s law
C) Gauss’s law applies to a closed surface of any shape
D) Gauss’s law states that the net number of lines crossing any closed surface in an outward
direction is proportional to the net charge enclosed within the surface
8) A physics instructor in an anteroom charges an electrostatic generator to 25 µC, then carries
it into the lecture hall. The net electric flux (in N m2/C) through the lecture hall walls is:
A) 0
B) can't tell unless the dimensions of the hall are given
C) 2.2 x 105
D) 2.8 x 106
9) A thick spherical conducting shell has charge Q. A particle with charge q is placed at the center of
the cavity. Then the charge on the inner surface of the shell and the charge on the outer surface of
the shell, respectively, are:
A) 0, Q
B) q, Q - q
C) Q, 0
D) - q, Q +q
10) A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. If the charge
on each plate has a magnitude of 4 x 10-6 C the potential difference (in volts) across the plates is
approximately:
A) 4 x 10-2
B) 4 x 108
C) 2 x 102
2
D) 1 x 102
11) The capacitance of a cylindrical capacitor (i.e., two concentric conducting cylinders of equal
length, one inside the other) can be increased by:
A) decreasing the radius of the inner cylinder and increasing the radius of the outer cylindrical
B) decreasing both the radius of the inner cylinder and the length
C) increasing both the radius of the inner cylinder and the length
D) increasing the radius of the outer cylindrical shell and decreasing the length
12) Let Q denote charge, V denote potential difference, and U denote stored energy. Of these
quantities, two capacitors in series must have the same:
A) Q only
B) V only
C) U only
D) Q and U only
13) Two particles with charges Q and − Q are fixed at the vertices of an equilateral triangle with sides
of length a, as shown.
If k = 1/4πε0, the work required to move a particle with charge q from the third vertex to point
midway along the line joining Q and - Q is:
A) 0
B) kQq/a
C) 2kQq/a
3
D)
2kqQ/a
14) Capacitor C1 is connected alone to a battery and charged until the magnitude of the charge on each
plate is 4.0 x 10-8 C. Then it is removed from the battery and connected to two other capacitors C2
and C3 as shown.
The charge on the positive plate of C1 is then 1.0 x 10-8 C. . The charges on the positive plates of
C2 and C3 are:
A) q2 = 2.0 x 10-8 C and q3 = 2.0 x 10-8 C
C) q2 = 3.0 x 10-8 C and q3 = 3.0 x 10-8 C
B) q2 = 5.0 x 10-8 C and q3 = 1.0 x 10-8 C
D) q2 = 3.0 x 10-8 C and q3 = 1.0 x 10-8 C
15) The figure shows four 6-µF capacitors.
The capacitance (in µF) between points a and b is:
A) 3
B) 4
C) 6
D) 9
16) A parallel-plate capacitor has a plate area of 0.3 m2 and a plate separation of 0.1 mm. If the
charge on each plate has a magnitude of 5.0 x 10-6 C then the force exerted by one plate on the
other has a magnitude (in N) of about:
A) 0
B) 5.0
C) 9.5
4
D) 1.0 x 104
17) Two conductors are made of the same material and have the same length. Conductor A is a
solid wire of diameter 1cm. Conductor B is a hollow tube of inside diameter 1cm and outside
diameter 2 cm. The resistance ratio RA/RB of the two conductors is:
A) 1
B)
C) 3
2
D) 4
18) The magnetic field at any point is given by B = A r x k , where r is the position vector of the
point, A is a constant, and k the unit vector in the z direction The net current through a circle of
radius R, in the xy plane and centered at the origin, is:
A) πAR2/µ0
B) πAR/µ0
C) 4πAR3/3µ0
D) 2πAR2/µ0
19) The emf that appears in Faraday's law is:
A) around a conducting circuit
B) perpendicular to the surface used to compute the magnetic flux
C) throughout the surface used to compute the magnetic flux
D) around the boundary of the surface used to compute the magnetic flux
20) In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed.
When switch S is then opened, the circuit has a time constant τa. Conversely, suppose S is initially
open. When it is then closed, the circuit has a time constant τb. The ratio τa/τb is:
A) 1
B) 2
C) 0.5
5
D) 0.67
21) The circuit shown was wired for the purpose of measuring the resistance of the lamp L.
Inspection shows that:
A) the ammeter A should be in parallel with R, not L
B) R and L should be interchanged
C) the meters, V and A, should be interchanged
D) L and V should be interchanged
22) A permanent magnet moves inside a coil. Considering the following factors:
I. strength of the magnet
II. number of turns in the coil
III. speed at which the magnet moves,
which can affect the emf induced in the coil?
A) I only
B) II only
C) I and II only
D) I, II, and III
23) This problem relates to Fig. 2 on the Figures Page. An inductance L, resistance R, and ideal
battery of emf E are wired in series. A switch in the circuit is closed at time 0, at which time the
current is zero. At any later time t the magnitude of the emf of the inductor is given by:
A) E(1 - e-Lt/R)
B) Ee-Lt/R
C) E(1 + e-Rt/L)
D) Ee-Rt/L
24) This problem relates to Fig. 3 on the Figures Page. The diagrams show three circuits with identical
batteries, identical inductors, and identical resistors. Rank them according to the current through
the battery just after the switch is closed, from least to greatest.
A) 3, 2, 1
B) 3, 1, 2
C) 1, 3, 2
6
D) 1, 2, 3
25) The stored energy in an inductor:
A) depends, in sign, upon the direction of the current
B) depends on the rate of change of current
C) is proportional to the square of the inductance
D) none of the above
26) This problem relates to Fig. 2 on the Figures Page. An inductance L and a resistance R are
connected in series to an ideal battery. A switch in the circuit is closed at time 0, at which time the
current is zero. The energy stored in the inductor is a maximum:
A) a long time after the switch is closed
B) just after the switch is closed
C) at the time t = L/R after the switch is closed
D) at the time t = 2L/R after the switch is closed
27) This problem relates to Fig. 4 on the Figures Page. A charged capacitor and an inductor are
connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period
of the resulting oscillations, the next time after t = 0 that the magnitude of the voltage across the
inductor is a maximum (i.e., irrespective of sign) is:
A) T
B) T/4
C) T/2
D) 2T
28) This problem also relates to Fig. 4 on the Figures Page. A charged capacitor and an inductor are
connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period
of the resulting oscillations, the next time after t = 0 that the energy stored in the magnetic field of
the inductor is a maximum is:
A) T
B) T/4
C) T/2
D) 2T
29) An LC circuit has an inductance of 20mH and a capacitance of 5.0 µF. At time t = 0 the
charge on the capacitor is 3.0 µC, and the current is 7.0 mA. The total energy (in units of 10-7 J) is:
A) 4.1
B) 5.2
C) 9
D) 14
30) The angular frequency of a certain RLC series circuit is ω0. A source of sinusoidal emf, with
angular frequency 2 ω0, is inserted into the circuit. After transients die out the angular frequency
of the current oscillations is:
A) ω0/2
B) ω0
C) 2ω0
7
D) 1.5ω0
31) Consider the circuit shown below.
Immediately after switch S in the circuit shown is closed, the current through the battery will be:
A) 0
C) V0/(R1 + R2)
B) V0/R1
D) V0(R1 + R2)/R1R2
32) Consider the circuit shown below.
The total impedance of the circuit (in ohms) is:
A) 65
B) 21
C) 50
8
D) 98
33) A coil has a resistance of 60 Ω and a total impedence (i.e., including its reactance) of 100 Ω. Its
reactance, in ohms, is:
A) 40
B) 60
C) 117
D) 80
34) This problem relates to Fig. 5 on the Figures Page, which shows Maxwell's Equations. Which of
those equations, along with a symmetry argument, can be used to calculate the magnetic field
between the plates of a charging parallel plate capacitor with circular plates?
A) Equation II
B) Equation III
C) Equation IV
9
D) Equation I
Answer Key
Testname: GF F.VIII
1) D
2) C
3) A
4) B
5) C
6) C
7) A
8) D
9) D
10) C
11) C
12) A
13) A
14) C
15) C
16) B
17) C
18) D
19) D
20) B
21) C
22) D
23) D
24) C
25) D
26) A
27) C
28) B
29) D
30) C
31) C
32) A
33) D
34) C
10