### Spring 2009 Physics 212 Hour Exam 1(24 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 102. The exam period was 90 minutes; the mean score was 74.3; the median was 76. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

Consider the two spherical shell capacitors shown in this diagram. The outer shells of both capacitors have a radius b. The inner shell of C1 has radius a; the inner shell of C2 has radius 2a. What is the relationship between the values of the capacitances C1and C2?

(a)   C1 < C2
(b)   C1 = C2
(c)   C1 > C2

### QUESTION 2***

Consider the two spherical shell capacitors shown in this diagram. The two capacitors are the same in every way except that capacitor C2 has twice the charge on its plates as capacitor C1. Compare the capacitance of C1 and C2.

(a)   C2 = (1/2) C1
(b)   C2 = C1
(c)   C2 = 2 C1

### QUESTION 3*

This and the next three questions pertain to the following situation.

Four capacitors are connected as shown and connected to a battery to maintain a constant potential difference between points a and b. A charge Q2 = 61.6 μC is measured on capacitor 2.

Calculate the energy stored in capacitor 2?

(a)   U2 = 57 μJ
(b)   U2 = 83 μJ
(c)   U2 = 95 μJ

### QUESTION 4*

What is the effective capacitance of this network of capacitors?

(a)   Ceff = 3.4 μF
(b)   Ceff = 6.7 μF
(c)   Ceff = 18 μF
(d)   Ceff = 25 μF
(e)   Ceff = 37 μF

### QUESTION 5*

What is the charge on capacitor C3?

(a)   Q3 = 5.9 μC
(b)   Q3 = 11.6 μC
(c)   Q3 = 18.9 μC
(d)   Q3 = 26.4 μC
(e)   Q3 = 62.5 μC

### QUESTION 6***

If the space between the plates of capacitor C4 is filled with a dielectric (k = 2) while the capacitors remain connected to the battery, what happens to the voltage across capacitor 1?

(a)   V1 increases.
(b)   V1 remains unchanged.
(c)   V1 decreases.

### QUESTION 7*

The charge configuration at the right consists of a uniformly charged rod that is bent into the shape of a ring having radius R and total positive charge Q. What is the magnitude of the electric field at the center of the ring?

(a)
(b)
(c)

### QUESTION 8**

The charge configuration at the right consists of an insulating rod that is bent into the shape of a quarter-circle having total positive charge Q distributed uniformly over its length. Suppose that the magnitude of the total electric field at the origin due this charge configuration is E0.

In terms of E0, what would be the total electric field vector at the origin due to the semi-circle of charge shown below? The left quarter-circle has negative charge, -Q, distributed uniformly and the right quarter-circle has positive charge, Q, distributed uniformly.

(a)
(b)
(c)
(d)
(e)

### QUESTION 9**

This and the next question are about the following situation:

An insulating sphere of radius R has positive charge uniformly distributed throughout its volume. The volume charge density (i.e., the charge per volume) is ρ.

What is the flux through a Gaussian spherical shell of radius R/2 that is totally contained inside the charged sphere and centered a distance R/2 from the center of the charged sphere, as shown by the dashed sphere in the diagram below?

(a)
(b)
(c)

### QUESTION 10**

Now surround the original (from the previous question) positively charged insulating sphere with a concentric insulating shell of inner radius R and outer radius 2R (as shown in the picture below). The insulating shell is negatively charged and has volume charge density ­ρ. Which one of the five graphs below best describes the electric field as a function of the radius, r ?

(a)
(b)
(c)
(d)
(e)

### QUESTION 11*

This and the next question are about the following situation:

Three different set-ups are shown below. The set-ups consist of either charged rods or point charges (or both). All rods have length 2a and charge +Q or -Q distributed uniformly. All charges are of magnitude Q, with some positive and some negative as indicated.

Which set-up has the largest magnitude electric field at the origin?

(a)   set up #1
(b)   set up #2
(c)   set up #3

### QUESTION 12**

Which set-up has the largest electric potential at the origin?

(a)   set up #1
(b)   set up #2
(c)   set up #3

### QUESTION 13*

A point charge, Q, is placed at the center of a spherical Gaussian surface, as shown. The total flux through the surface is Φ In which one of the following cases does the total flux Φ through the surface change?

(a)
(b)
(c)
(d)
(e)

### QUESTION 14*

The electric field in a region of space is described by the electric field line pattern shown. The two small "x" denote two different points in the field, labeled A and B. A positive point charge is moved from point A to point B. Which statement below is valid about the work done by the electric field when the charge is moved from A to B?

(a)   The work done is positive.
(b)   The work done is negative.
(c)   The work done depends on the path taken from A to B.

### QUESTION 15*

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

Three point charges are placed on the coordinate system as shown.

What is the magnitude of the electric field at the origin due to all three charges?

(a)   |E| = 0
(b)   |E| = 4.18 × 107 N/C
(c)   |E| = 7.81 × 107 N/C
(d)   |E| = 1.07 × 107 N/C
(e)   |E| = 1.63 × 107 N/C

### QUESTION 16*

How much work did the electric field do as these charges were moved from infinitely far apart to the positions shown?

(a)   W = +3.63 J
(b)   W = +0.89 J
(c)   W = -1.72 J
(d)   W = -1.93 J
(e)   W = -3.92 J

### QUESTION 17**

Calculate the electric potential at the origin due to the three charges.

(a)   V = 7.39 × 106 J/C
(b)   V = 3.83 × 106 J/C
(c)   V = 2.25 × 106 J/C
(d)   V = 1.35 × 106 J/C
(e)   V = 1.13 × 106 J/C

### QUESTION 18**

This and the next question are about the following situation:

A ring of radius R and very small cross-section has a total charge +Q distributed uniformly on it. A point mass m carrying a charge -q is released from rest at a point P on the axis of symmetry of the ring a distance 2R from the ring's center.

Calculate the electric potential V due to the ring at the point P. (Assume V = 0 when infinitely far from the ring of charge.)

(a)
(b)
(c)

### QUESTION 19**

Calculate the kinetic energy Kf of the mass m when it reaches the center of the ring, assuming that it moves along the symmetry axis.

(a)
(b)
(c)

### QUESTION 20**

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

A nonconducting, solid sphere of radius a is placed at the center of a spherical conducting shell of inner radius b (> a) and outer radius c, as shown in the figure below. A charge +Q is distributed uniformly through the sphere, which thus carries a charge density ρ (C/m3). The outer shell carries a total charge -3Q.

Find the electric field E(r) within the solid sphere, i.e., at a radius r < a.

(a)
(b)
(c)

### QUESTION 21*

Find the electric field E(r) between the sphere and the shell (a < r < b).

(a)
(b)
(c)

### QUESTION 22*

Find the electric field E(r) inside the shell (b < r < c).

(a)
(b)
(c)

### QUESTION 23*

Now find the charge and its algebraic sign on the inner surface of the conductiing shell (r = b).

(a)   -3Q
(b)   -2Q
(c)   -Q
(d)   +2Q
(e)   +3Q

### QUESTION 24***

A thin, conducting plane which is very extended in the x and y directions is placed in an external electric field which points in the + z direction and has magnitude E (see figure below).

Find the charge density on the left surface of the metal plane.

(a)   σL = -2ε0E
(b)   σL = +2ε0E
(c)   σL = -ε0E
(d)   σL = +ε0E
(e)   σL = -E / 2ε0

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.