### Fall 2008 Physics 212 Hour Exam 1(27 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

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 119. The exam period was 90 minutes; the mean score was 91.6; the median was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1* An asymmetrical electric dipole consists of two opposite but unequal-strength electric charges, as shown in this figure.

Which one of the three diagrams given below shows the correct equipotential contours associated with this dipole? (a)
(b)
(c)

### QUESTION 2* The diagram at right depicts the electric field lines in a region of space. Compare the magnitude of the electric field at position A (EA) with the magnitude of the electric field at position B (EB).

(a)   EA < EB
(b)   EA = EB
(c)   EA > EB

### QUESTION 3* Two charges are placed on the y-axis to form a dipole as shown in the figure. Which of the following planes is an equipotential surface?

(a)   xy-plane
(b)   yz-plane
(c)   zx-plane

### QUESTION 4**

A parallel-plate capacitor is connected to a battery and charged up as shown. (The battery maintains a constant voltage V across the capacitor.)

With the battery still connected, the thick conducting slab shown at the right is placed symmetrically between the two plates. What is the effect on the capacitance C? (a)   C increases.
(b)   C remains the same.
(c)   C decreases.

### QUESTION 5*

This and the next question pertain to the following situation. A positive point charge +Q0 is located at point P a distance d from a large thin sheet with uniform positive charge density σo. A cylindrical Gaussian surface encloses the +Q0 charge and a portion of the sheet as shown.

Let Φo represent the outward flux through the curved side wall (the barrel) of the Gaussian surface. Which one of the following relations is correct?

(a)   Φo > 0
(b)   Φo = 0
(c)   Φo < 0

### QUESTION 6** A negative point charge -Q0 is now placed just outside the Gaussian surface as shown. Let Φbefore and Φafter represent the flux through the left end cap, before and after the charge -Q0 is introduced.

Which of the following describes how the magnitude of the net flux through the left end cap changes when the new charge is introduced?

(a)   | Φafter |  >  | Φbefore |
(b)   | Φafter |  =  | Φbefore |
(c)   | Φafter |  <  | Φbefore |

### QUESTION 7**

This and the next question are about the following situation:

Two charged rods, each with positive net charge Q0, are held in place as shown in the top view diagram below. A small positive test charge q0 travels from point A to point B along the circular arc shown. The work done on the charge by the electric field is

(a)   positive.
(b)   negative.
(c)   zero.

### QUESTION 8**

The positive test charge q0 is launched from point A with an initial velocity vA and is observed to pass through point B with a velocity vB. (The charge does not necessarily follow the path shown in the figure.) Compare the magnitude of the velocity at point A to that at point B.

(a)   | vA | > | vB |
(b)   | vA | = | vB |
(c)   | vA | < | vB |

### QUESTION 9**

This and the next three questions are about the following situation:

Three thick conducting infinite planes are oriented perpendicular to the x axis, and placed at the positions given in the figure below. Each plane carries a net charge, as indicated in the legend. A negatively charged object placed at x = +4 cm and released would experience a force in the positive x direction.

(T)   True
(F)   False

### QUESTION 10**

How many of the seven regions indicated in the figure have an electric field of zero?

(a)   1 region
(b)   3 regions
(c)   5 regions

### QUESTION 11*

Calculate the x component of the electric field at the origin.

(a)   Ex = 0
(b)   Ex = 3.39 × 105 N/C
(c)   Ex = 7.58 × 105 N/C
(d)   Ex = 11.5 × 105 N/C
(e)   Ex = 14.6 × 105 N/C

### QUESTION 12**

Calculate the charge density σL on the left side of the center slab (see figure).

(a)   σL = -6 μC/m2
(b)   σL = -3 μC/m2
(c)   σL = 0
(d)   σL = 3 μC/m2
(e)   σL = 6 μC/m2

### QUESTION 13***

This and the next two questions are about the following situation:

Consider an infinite line with charge density λ0 = +3 μC/m, shown in the center of the figure below. Concentric with the line is a hollow thick-walled cylinder (shaded), made of conducting material. The hollow cylinder carries a charge per unit length of λ = -3 μC/m. Finally, a thin nonconducting cylindrical shell is concentric with the other two objects, and carries a charge per unit length of λc = +6 μC/m. The dimensions of the objects are shown in the figure; all three have infinite length. What is the surface charge density σb on the outer surface of the thick conducting shell?

(a)   σb > 0
(b)   σb = 0
(c)   σb < 0

### QUESTION 14*

What is the magnitude of the electric field at a radius r = 20 cm ?

(a)   E = 0.54 × 106 N/C
(b)   E = 1.23 × 106 N/C
(c)   E = 3.15 × 106 N/C
(d)   E = 5.57 × 106 N/C
(e)   E = 7.14 × 106 N/C

### QUESTION 15**

Which of the following graphs best represents the radial dependence of the electric field E ? (a)
(b)
(c)
(d)
(e)

### QUESTION 16*

This and the next three questions are about the following situation:

Three massive charged balls are positioned as shown in the figure below. A frictionless rod running along the x axis constrains the motion of Ball #3 to slide along this axis. Ball #1 and Ball #2 are fixed on the y axis at + 4 cm and -4 cm, respectively. Ball #3 is initially located at x = 8 cm and is held fixed.

How much total energy is required to assemble these Balls into their initial positions assuming they all start off infinitely far away? (a)   Utotal = -3.11 J
(b)   Utotal = -1.59 J
(c)   Utotal = 0
(d)   Utotal = 2.34 J
(e)   Utotal = 8.94 J

### QUESTION 17**

Now imagine releasing Ball #3 from rest (remember, it can only move along the x axis). Ball #3 will

(a)   eventually come to rest at the origin.
(b)   oscillate back and forth along the x axis about the origin.
(c)   fly off to negative infinity along the x axis.

### QUESTION 18**

What is the electric potential V(0) at the origin, given that the potential V(∞) at infinity is defined to be zero?

(a)   V(0) = 0
(b)   V(0) = 0.94 × 105 J/C
(c)   V(0) = 2.15 × 105 J/C
(d)   V(0) = 5.63 × 105 J/C
(e)   V(0) = 7.42 × 105 J/C

### QUESTION 19*

What is the x component of the force exerted on Ball #3 by the other two balls?

(a)   Fx = -11.5 N
(b)   Fx = -18.1 N
(c)   Fx = -24.4 N
(d)   Fx = -30.7 N
(e)   Fx = -39.5 N

### QUESTION 20**

This and the next three questions are about the following situation:

A conducting sphere of radius a = 20 cm carries a charge of +6 μC. Concentric with this sphere is a non-conducting spherical shell with an inner radius of b = 70 cm and an outer radius of c = 80 cm. This shell carries a charge of -6 μC, distributed uniformly throughout the material of the shell. As one moves from a position very far from these two objects to a point just outside the nonconducting shell, the electric potential

(a)   increases.
(b)   decreases.
(c)   stays the same.

### QUESTION 21**

Consider the work Wcb required to move a positive test charge from the outer surface of the nonconducting shell to its inner surface. Which of the following is true?

(a)   Wcb > 0
(b)   Wcb = 0
(c)   Wcb < 0

### QUESTION 22*

What is the magnitude of the potential difference ΔVab between the outer surface of the conducting sphere and the inner surface of the nonconducting shell?

(a)   | ΔVab |  =  7.1 × 105 V
(b)   | ΔVab |  =  5.9 × 105 V
(c)   | ΔVab |  =  3.3 × 105 V
(d)   | ΔVab |  =  1.9 × 105 V
(e)   | ΔVab |  =  0

### QUESTION 23*

Consider a a positive test charge q = 15 μC placed at a radius of 40 cm from the center of the conducting sphere. What is the magnitude of the force F on this test charge?

(a)   F = 0
(b)   F = 2.31 N
(c)   F = 3.58 N
(d)   F = 5.06 N
(e)   F = 7.45 N

### QUESTION 24*

This and the next three questions are about the following situation:

Three capacitors are connected as shown in the figure below. The gaps between the plates of all three capacitors are filled with air (κ = 1.0), giving the capacitance values listed in the figure. A constant potential difference of 6 V is maintained between points A and B on the circuit.

What is the magnitude of the charge Q2 on each of the plates of capacitor C2? (a)   Q2 = 24 μC
(b)   Q2 = 12 μC
(c)   Q2 = 6 μC
(d)   Q2 = 3 μC
(e)   Q2 = 2 μC

### QUESTION 25*

What is the total energy Utot stored on the three capacitors?

(a)   Utot = 22.2 μJ
(b)   Utot = 33.7 μJ
(c)   Utot = 44.5 μJ
(d)   Utot = 55.3 μJ
(e)   Utot = 66.9 μJ

### QUESTION 26*

What is the potential difference V3 across the plates of capacitor C3?

(a)   V3 = 1.78 V
(b)   V3 = 2.60 V
(c)   V3 = 3.43 V
(d)   V3 = 4.04 V
(e)   V3 = 4.85 V

### QUESTION 27*

A dielectric material with κ = 5.4 is now inserted between the plates of capacitor C2. What is the change in the amount of energy stored on this capacitor?

(a)   | ΔU2 |  =  76.4 μJ
(b)   | ΔU2 |  =  158 μJ
(c)   | ΔU2 |  =  267 μJ
(d)   | ΔU2 |  =  378 μJ
(e)   | ΔU2 |  =  480 μJ

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.