Physics 2B, Electricity and Magnetim -- Winter 2009
Final Exam
Instructor: B. Grinstein
INSTRUCTIONS: Fill, tear and return the bottom strip of the front page with your scantron. Keep the top portion of the front page and the rest of the quiz. Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER".
Bubble in the quiz form (see letter A--D at bottom of page) in your scantron under "TEST FORM"
Useful numbers: K = 9.0 109 Nm2/C2, o = 8.85 10-12 C2/Nm2, e = 1.60 10-19 C, me = 9.11 10-31 kg
µ o = 4 10-7 T m/A
1) For the circuit shown in the figure below, which equation is correct for loop 2 (going clockwise)?
A) E2 + R3I3 + E3 - R2I2 = 0
B) E2 - R3I3 - E3 - R2I2 = 0
C) E2 + R3I3 - E3 + R2I2 = 0
D) E2 + R3I3 + E3 + R2I2 = 0
E) -E2 + R3I3 - E3 + R2I2 = 0
2) Consider two wires made of different materials. Wire 1 carries a current I and has a cross-sectional area A. Wire 2 carries a current 2I and has a cross-sectional area A/2. Under what condition would the electrons in the two wires have equal drift velocities?
A) If the electron concentration in wire 2 is four times the electron concentration in wire 1
B) If the electron concentrations in the two materials are the same
C) If the electron concentration in wire 2 is twice the electron concentration in wire 1
D) If the electron concentration in wire 1 is twice the electron concentration in wire 2
E) If the electron concentration in wire 1 is four times the electron concentration in wire 2
3) An electron beam moving horizontally at a speed v0 enters a region between two horizontally oriented plates of length
L1. When the electrons reach a fluorescent screen located at a distance L2 past these plates, they have been deflected a vertical distance y from their original direction. If the speed of the electrons is doubled what is the new value of the deflection?
A) 2y B) y C) y/4 D) 4y E) y/2
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Name________________________________________ Quiz ID_________________________ exam version D-1

4) The figure below shows equipotentials surrounding a pair of charges QA and QB. The value of the potential half-way between the charges is indicated. Which of the statements below applies to the charges?
A) The two charges have the same sign but different magnitudes.
B) The two charges have the same sign and equal magnitudes.
C) Nothing can be said about the charges.
D) The two charges have opposite signs and different magnitudes.
E) The two charges have opposite signs and equal magnitudes.
5) An RLC circuit is operating with a phase angle of 30°. When the frequency is increased, the phase angle ________
A) varies in an indeterminable way.
B) decreases.
C) stays the same.
D) varies in a determinable way.
E) increases.
6) The figure below shows the variations of the electric potential V (in arbitrary units) as a function of the position x (also in arbitrary units). Which of the choices below correctly describes the orientation of the electric field along the x axis?
0.5
1 1.5
A) E is positive from x = -2 to x = 2.
B) E is positive from x = -2 to x = 0, and negative from 0 to x= 2.
C) E is negative from x = -2 to x = 2.
D) E is negative from x = -2 to x = 0, and positive from 0 to x= 2.
E) More information is needed to answer the question.
exam version D-2

7) The figure below shows 3 long, parallel, current-carrying wires. The current directions are indicated for currents I1 and
I3. The arrow labeled F represents the magnetic force acting on current I3. The 3 currents have equal magnitudes. What is the direction of the current I2?
A) horizontal to the right
B) into the picture (in the direction opposite to that of I1 and I3)
C) out of the picture (in the same direction as I1 and I2)
D) vertical downward
E) vertical upward
8) Starting from zero, an electric current is established in a circuit made of a battery of emf E, a resistor of resistance R and an inductor of inductance L. The electric current eventually reaches its steady-state value. What would be the effect of using a resistor with a higher resistance in this circuit?
A) The steady-state value of the current would be smaller, but it would take the same amount of time to reach it.
B) The steady-state value of the current would be larger, but it would take more time to reach it.
C) The steady-state value of the current would be smaller, but it would take more time to reach it.
D) The steady-state value of the current would be smaller, but it would take less time to reach it.
E) The steady-state value of the current would be larger, but it would take less time to reach it.
9) Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?
A) One is positive and the other either positive or uncharged
B) One is positive and the other is uncharged
C) Both are positive
D) One is positive and the other is negative
E) None of the above
exam version D-3

10) The figure below shows 3 identical light bulbs connected to a battery. What happens to the brightness of light bulb 1 when the switch S is closed?
A) The brightness decreases.
B) The brightness increases.
C) The brightness will increase momentarily then return to its previous level.
D) The brightness will decrease momentarily then return to its previous level.
E) The brightness remains the same as before the switch is closed.
11) Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Plate A has a uniform, positive charge density of magnitude A. Plate B has a uniform, negative charge density of magnitude B . What is the magnitude of the electric field half-way between the two charges?
A) E = 0
B) E = ( AB )/ 0
C) E = ( AB )/2 0
D) E = ( A+ B )/2 0
E) E =( A+ B )/ 0
12) Charges A and B exert repulsive forces on each other. qA = 4qB and they have equal masses. Which statement is true?
A) The force that A exerts on B is equal in magnitude to the force that B exerts on A.
B) The force that A exerts on B is 4 times smaller than the force that B exerts on A.
C) The force that A exerts on B is 4 times larger than the force that B exerts on A.
D) The relative size of the forces depends on the distance between the charges.
E) Two of the above
exam version D-4

13) The graph below shows the variation of the electric potential V (measured in Volts) as a function of the radial direction r
(measured in meters). For which range of r is the magnitude of the electric field the largest?
1 2 3 4 5 6 7
A) from r = 2 m to r = 4 m
B) from r = 0 to r = 2 m
C) from r = 4 m to r = 6 m
D) The magnitude of the field is the same everywhere.
E) More information is needed to answer the question.
14) A capacitor of capacitance C = 5 µ F is connected in series with a resistor R = 3 M to a battery of emf E = 20 V. What is the value of the current in the circuit when the capacitor has reached 50% of its maximum charge?
A) 6.2 µ A B) 1.7 µ A C) 3.3 µ A D) 0.51 µ A E) 9.2 µ A
15) A circular loop of wire of area 25 cm2 lies in the plane of the paper. A decreasing magnetic field B is coming out of the paper. It continues decreasing, until it vanishes and then increases, pointing in the opposite direction (into the paper).
What is the direction of the induced current in the loop?
A) clockwise
B) clockwise then counterclockwise
C) counterclockwise
D) counterclockwise then clockwise
E) There is no current.
16) A long line of charge with charge per unit length 1 is located on the x-axis and another long line of charge with charge per unit length 2 is located on the y-axis with their centers crossing at the origin. In what direction is the electric field at point z = a on the positive z-axis if 1 and 2 are positive?
A) the positive z-direction
B) all directions are possible parallel to the x-y plane
C) the negative z-direction
D) halfway between the x-direction and the y-direction
E) cannot be determined
17) If a coaxial cable is carrying a current, where will the magnetic energy density be the greatest?
A) 70.7% of the way between the conductors
B) half-way between the two conductors
C) 33% of the way between the conductors
D) near the inner conductor
E) near the outer conductor
exam version D-5

18) An AC generator consists of a coil with 50 turns of wire, each with an area of 0.02 m2. The coil rotates in a uniform magnetic field B = 0.4 T at a constant frequency of 60Hz and produces an average power of 50 W. What is the resistance of the coil?
A) 53 B) 85 C) 2.4 D) 150 E) 227
19) A 1 mF, a 2 mF, and a 3 mF capacitor are connected in series, the combination being connected across a 9 volt battery.
The capacitor with the greatest charge on it is
A) the 3 mF.
B) the 2 mF.
C) the 1 mF.
D) cannot be determined
E) They all have the same charge.
20) A charged capacitor of capacitance C and an inductor of inductance L are connected to form an LC circuit. At time t =2 s after the connection is made, the charge on the capacitor is equal to zero for the first time. If a capacitor of capacitance
C2= 2C and an inductor of inductance L2 = 2L are connected in a similar manner, how long will it take for the capacitor to be fully discharged the first time?
A) 4 s B) 0.5 s C) 2 s D) 1 s E) 8 s
21) Three electric charges of equal magnitudes are positioned along the y-axis. The figure below shows electric field lines near the charges. What can be said about the signs of the charges?
A) Q1 and Q3 are negative and Q2 is positive.
B) The 3 charges are negative.
C) The 3 charges are positive.
D) Q1 and Q3 are positive and Q2 is negative.
E) The 3 charges have the same sign.
exam version D-6

22) In the figure below the values of the resistances are 50 for resistor A, 100 for resistor B, and 300 for resistor C.
The battery has a voltage V = 5 V. What is the power delivered by the battery?
A) 1.5 W B) 0.15
C) 0.25 W D) 2.5 W E) 0.45 W
23) The figure below shows 4 different sets of wires that cross each other without actually touching. The magnitude of the current is the same in all four cases, and the directions of current flow are as indicated. For which configuration will the magnetic field at the center of the square formed by the wires be equal to zero?
A) A
B) B
C) C
D) D
E) The field is equal to zero in all four cases.
24) The direction of the electric field halfway between an electron and a proton is
A) perpendicular to the line from the electron to the proton
B) undefined since the electric field is zero
C) toward the proton
D) toward the electron
E) cannot be determined
exam version D-7

25) A hollow conducting sphere has radii of 0.80 m and 1.20 m. The sphere carries a charge of -500 nc.
A point charge of +300 nC is present at the center. The radial component of the electric field at a point which is 1.50 m from the center is closest to:
A) -1600 N/C B) -800 N/C C) -2000 N/C D) +2000 N/C E) +1200 N/C
26) When a parallel-plate capacitor of capacitance C is connected to a battery of voltage V, the energy density in the capacitor is u. If the voltage of battery is doubled, which of the following changes would keep the energy density equal to its previous value u?
A) doubling the size of the plates
B) doubling the spacing of the plates
C) reducing the spacing of the plates
D) reducing the size of the plates by half
E) The energy density is unaffected by a change in the voltage.
27) Two metal spheres of radii R1 and R2 carry an equal electric charge Q. The spheres are at potentials V1 and V2 respectively with V1 = 3V2. The spheres are then connected by a conducting wire. When equilibrium is reached, what is the charge on the sphere of radius R2?
A) Q/2 B) 3Q/2 C) Q D) Q/3 E) 2Q
28) A circular loop of wire has a current I flowing around it. The radius of the loop is R. A magnetic field of magnitude B is turned on in the direction perpendicular to the plane of the loop (oriented as the normal to the loop using the right hand rule given the direction of the current). The net force on the loop has a magnitude
A) IBR/2.
B) 4IBR.
C) 2IBR.
D) IBR/4 E) 0.
29) A charge Q distributed uniformly along the edge of a ring of radius R. What is the electric potential due to this charge at a distance x = R from the center the ring along its axis?
A)
4
1
0
Q
R
B)
4
1
0
Q
R2
C)
4
1
0
Q
2R
D)
4
1
0
Q
2R
E) 0
exam version D-8

30) The figure below shows 3 metallic frames labeled A, B, and C heading towards a region where a uniform magnetic field exists. The frames move with the same constant velocity. Their relative sizes are indicated by the background grid. As they enter the magnetic field the frames will have an induced electric current along their perimeter. Rank order the loops by the magnitude of their induced currents, smallest to largest.
A) IA = IB = IC 0
B) IA = IB < IC
C) IA < IB = IC
D) IA < IB < IC
E) There is no induced current when the frames move at constant speed.
exam version D-9

31) A voltmeter is used to measure the voltage across a Hall strip conducting a current in the negative y-direction as shown in the figure below. The charge carrier are known to be positive in this strip. What is the direction of the magnetic field used in this experiment if the reading on the voltmeter is negative when the probes are connected as shown? (Note: a voltmeter shows a positive reading when the terminal labelled "+" is at a higher potential than the terminal labelled "-").
A) positive y direction
B) negative z direction
C) positive x direction
D) negative x direction
E) positive z direction
32) An AC source of period T and maximum voltage V is connected to a single unknown element. At time t = 0 the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I =
- Imax where Imax is the current amplitude. What is the unknown element?
A) an inductor or a capacitor
B) an inductor
C) a capacitor
D) a resistor
E) More information is needed to identify the element.
33) Three negative charges of equal magnitudes are positioned along the x-axis at x = -a, x=0, and x = +a respectively. The charge located at x=0 is moved away along the y-axis to a position (x,y) = (0, +a). How does the potential energy of the system of charges change as a result?
A) The potential energy may increase or decrease depending on the magnitude of the charges.
B) The potential energy decreases.
C) The potential energy increases.
D) The potential energy stays the same.
E) More information is needed to answer the question.
34) What is the average power dissipated by a resistor of resistance 10 in a series RLC circuit for which the power factor is equal to 0.5, the capacitor has capacitance 9.0 mF, the inductor has inductance 2.7 mH and the maximum voltage of the AC source is 5 V?
A) 0.62 W B) 0.31 W C) 2.5 W D) 1.2 W E) 0.15 W
exam version D-10

35) A spherical, non-conducting shell of inner radius r1= 25 cm and outer radius r2= 30 cm carries a total charge Q = 30
µ C distributed uniformly throughout its volume. What is the magnitude of the electric field at a distance r= 27 cm from the center of the shell?
A) 1.32 106 N/C
B) 2.64 106 N/C
C) 0
D) 1.32 103 N/C
E) 2.64 103 N/C
exam version D-11

25) B
26) B
27) B
28) E
29) C
30) B
31) B
32) C
17) D
18) E
19) E
20) A
21) E
22) C
23) C
24) D
33) B
34) D
35) A
9) E
10) B
11) D
12) A
13) A
14) C
15) C
16) A
1) C
2) A
3) C
4) E
5) E
6) B
7) B
8) D
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Name________________________________________ Quiz ID_________________________ exam version D-12