### Fall 2009 Physics 212 Hour Exam 1(25 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 101. The exam period was 90 minutes; the mean score was 75.4; the median was 78. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

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

Four charges rest at the four corners of a rectangle with sides d and 2d. Two charges are positive and two charges are negative. (q = 2 C, d = 10 cm)

The electric potential is the same along the entire y-axis as it is in the center (point A) of the rectangle.

(T)   True
(F)   False

### QUESTION 2*

For which of the following positions is the magnitude of the electric field largest?

(a)   very close to points P1, P2, P3 and P4
(b)   at x = y = 0
(c)   at coordinates (x, y) = (0, d/2)

### QUESTION 3**

In fact, we have two superimposed dipoles offset by a distance d from each other. Knowing this, where is the y-component of the electric field zero? (This may not be the only region where Ey = 0.)

(a)   in the y-z plane (at x = 0)
(b)   in the x-z plane (at y = 0)
(c)   in the x-y plane (at z = 0)

### QUESTION 4*

This and the next question are about the following situation:

Consider a spherical Gaussian surface of radius r centered on a point charge Q, as shown above. As the radius r increases the total electric flux through the Gaussian surface also increases.

(T)   True
(F)   False

### QUESTION 5*

(a)   charge.
(b)   surface area to a Gaussian surface.
(c)   dimensions to space.

### QUESTION 6**

This and the next question are about the following situation:

An infinitely long, cylindrical conducting wire of radius a has a surface charge density σ (charge/unit area).

What is the magnitude of the electric field, E(r), outside the wire at a radial distance r from the wire's center?

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

### QUESTION 7*

Suppose σ > 0. If a positive charge is placed near the wire and released, it will move

(a)   parallel to the wire.
(b)   radially away from the central axis of the wire.
(c)   radially toward the central axis of the wire.

### QUESTION 8*

This and the next question are about the following situation:

Two point charges are placed on the x-axis as shown. Let Q = 3 μC and a = 5 m.

The y component of the electric field at point A is zero.

(T)   True
(F)   False

### QUESTION 9**

The magnitudes of the electric field at point A and point B are EA and EB, respectively. What is the ratio of EA over EB?

(a)   EA / EB  =  0
(b)   EA / EB  =  0.64
(c)   EA / EB  =  0.80
(d)   EA / EB  =  1.13
(e)   EA / EB  =  1.35

### QUESTION 10*

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

The figure below shows three flat plates, all of very large area. The two thin plates are made of insulating material and carry uniformly-distributed surface charge densities of σa and σb respectively. The thick metal plate has width w, and is initially uncharged.

What is the magnitude of the electric field EA at the origin (the point marked A on the figure)?

(a)   |EA| = 1.4 × 105 N/C
(b)   |EA| = 2.8 × 105 N/C
(c)   |EA| = 5.6 × 105 N/C

### QUESTION 11**

What is the sign of the surface charge density σLHS on the left-hand side of the thick metal plate?

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

### QUESTION 12**

Compare the electric potential Va at the location of the left-hand insulating plate (x = +d1) with the potential Vb at the location of the right-hand plate (x = d1 + d2).

(a)   Va < Vb
(b)   Va = Vb
(c)   Va > Vb

### QUESTION 13***

A student is told to add some charge Qmetal to the metal slab so that the magnitude of the potential difference |ΔVab| between the two insulating plates is exactly 50 kV. What should the student do?

(a)   Add negative charge to the metal slab.
(b)   Add positive charge to the metal slab.
(c)   Changing the charge on the metal slab will not affect the potential difference ΔVab.

### QUESTION 14*

This and the next question are about the following situation:

Two charges, +Q and -Q (equal in magnitude but opposite in sign) are fixed at a distance a from the origin on the x-axis. Point B is located at a distance b from the origin on the y-axis, and point C is located a distance c to the right of the charge +Q.

Now, a charge, q3 = +1 μC, is brought in from infinity and placed at point B. The total potential energy of the charge collection

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

### QUESTION 15*

A fourth charge, q4 = +2 μC, is now placed at point C. The charge q4 is released from rest, while the other three charges are held fixed. Given that the mass of q4 is m4 = 0.1 kg, find the speed v of q4 after it has traveled very far away from the other charges (i.e. to infinity).

(a)   v = 33.84 m/s
(b)   v = 0 m/s
(c)   v = 8.25 m/s
(d)   v = 14.41 m/s
(e)   It does not travel away from the charges.

### QUESTION 16*

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

A point charge Q is located at the center of a thick conducting spherical shell with inner radius a1 and outer radius a2. The shell has zero total charge. A thin spherical shell of non-conducting material radius a3 with uniform surface charge density surrounds the conductor. The net charge on the non- conductor is QNC.

Calculate the radial component of the total electric field at a radius 15 cm from the center of symmetry. (In the answer list below, a plus sign denotes a field that points radially outward, a minus sign the opposite direction.)

(a)   E = + 7.20 × 106 V/m
(b)   E = + 4.80 × 106 V/m
(c)   E = + 3.60 × 106 V/m
(d)   E = - 2.40 × 106 V/m
(e)   E = - 5.60 × 106 V/m

### QUESTION 17*

Calculate σ2 the surface charge density on the outer surface of the conducting shell.

(a)   σ2 = +398 μC/m2
(b)   σ2 = +154 μC/m2
(c)   σ2 = 0 μC/m2
(d)   σ2 = -298 μC/m2
(e)   σ2 = -326 μC/m2

### QUESTION 18**

Calculate the electric potential at the outer surface of the conductor, given that the potential at infinity is zero.

(a)   VC = - 6.74 × 105 V
(b)   VC = - 5.20 × 105 V
(c)   VC = 0 V
(d)   VC = + 3.26 × 105 V
(e)   VC = + 4.50 × 105 V

### QUESTION 19*

Three charges are arranged as shown. All three charges have a value of Q = +1 μC. Distances are in meters.

What is the magnitude of the force on charge Q1?

(a)   6.75 × 10-3 N
(b)   9.28 × 10-3 N
(c)   10.06 × 10-3 N
(d)   11.25 × 10-3 N
(e)   12.73 × 10-3 N

### QUESTION 20*

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

Four capacitors, a battery and a switch are assembled in the circuit below. Initially, the switch is set to position A and C4 is uncharged.

Find U, the total energy stored in the capacitors.

(a)   U = 14 mJ
(b)   U = 26 mJ
(c)   U = 30 mJ
(d)   U = 45 mJ
(e)   U = 55 mJ

### QUESTION 21*

Choose the statement that correctly relates Q1, Q2 and Q3, the charges on capacitors C1, C2 and C3, respectively.

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

### QUESTION 22*

At t = 0, the switch is moved to B.

When the switch is moved from A to B, C1 and C2 are discharged.

(T)   True
(F)   False

### QUESTION 23**

Find Q4, the charge on C4 when the switch is on B.

(a)   Q4 = 83 μC
(b)   Q4 = 162 μC
(c)   Q4 = 200 μC
(d)   Q4 = 222 μC
(e)   Q4 = 320 μC

### QUESTION 24*

This and the next question are about the following situation:

This figure shows the electric field lines for a system of two point charges, A and B. Three positions, labeled 1,2,3 are also marked.

Which one of the following is correct?

(a)   A is positive and smaller in magnitude than B.
(b)   A is negative and larger in magnitude than B.
(c)   A is negative and smaller in magnitude than B.

### QUESTION 25*

For the three positions shown (1,2,3), rank order the magnitude of the electric field, from strongest to weakest.

(a)   1 > 2 > 3
(b)   3 > 2 > 1
(c)   2 > 1 > 3

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.