### Fall 2007 Physics 102 Hour Exam 1(28 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 123. The exam period was 90 minutes; the mean score was 73.3 the median was 73. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

### QUESTION 1**

This and the next two questions pertain to the following situation:

Two charges are located on the x axis as shown in the figure.

d = 15 cm
q1 = -2 μC
q2 = +3 μC

What is the electrostatic energy U of the system comprised of charges q1 and q2 ?

(a)   U = -2.4 J
(b)   U = -0.36 J
(c)   U = 0
(d)   U = +0.36 J
(e)   U = +2.4 J

### QUESTION 2**

What charge q3 needs to be placed at position (x,y) = (3d,0) such that the magnitude of the electric field at the origin (E(0,0)) is zero?

(a)   q3 = -24.75 μC
(b)   q3 = -11.2 μC
(c)   q3 = -2 μC
(d)   q3 = 11.2 μC
(e)   q3 = 24.75 μC

### QUESTION 3**

q3 is now moved back to infinity. What charge q4 needs to be placed at position (3d,0) such that the magnitude of the electric potential at the origin (V(0,0)) is zero?

(a)   q4 = -11.2 μC
(b)   q4 = -2 μC
(c)   q4 = -1.5 μC
(d)   q4 = 1.5 μC
(e)   q4 = 11.2 μC

### QUESTION 4*

This and the next two questions pertain to the following situation:

Given is a map of equal-potential lines (see figure below). The potential is created by three charges in a plane (q1, q2, q3). Potential values are given in V. Note the signs (+/-).

Based on the map, what is the sign (+/-) of the charge q3 ?

(a)   -
(b)   0
(c)   +

### QUESTION 5**

Based on the map, what is the direction of the electric field at point B?

(a)   left
(b)   right
(c)   up
(d)   down
(e)   cannot be determined

### QUESTION 6**

How much work W is required for you to move a charge of 1 C from point C to point D?

(a)   W = -5 J
(b)   W = 0 J
(c)   W = 5 J

### QUESTION 7**

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

Given are 4 charges on a square of side a = 25 cm (see figure above). q = 1 μC.

What is the x component of electric field at the center of the square (Ex)?

(a)   Ex = -611,000 N/C
(b)   Ex = -204,000 N/C
(c)   Ex = 0 N/C
(d)   Ex = 204,000 N/C
(e)   Ex = 611,000 N/C

### QUESTION 8**

What is the y component of electric field at the center of the square (Ey)?

(a)   Ey = -611,000 N/C
(b)   Ey = -204,000 N/C
(c)   Ey = 0 N/C
(d)   Ey = 204,000 N/C
(e)   Ey = 611,000 N/C

### QUESTION 9**

What is the electric potential V at the center of the square?

(a)   V = -288,000 V
(b)   V = -51,000 V
(c)   V = 0 V
(d)   V = 51,000 V
(e)   V = 288,000 V

### QUESTION 10**

How much work W is required by you to move the top left charge (2q) from its position to the center of the square?

(a)   W = -0.22 J
(b)   W = -0.11 J
(c)   W = 0 J
(d)   W = 0.11 J
(e)   W = 0.22 J

### QUESTION 11*

This and the next two questions pertain to the following situation:

A small sphere of mass m = 0.4 grams is positioned in the middle between two capacitor plates (see figure above). The sphere is charged and at rest. The plates are horizontal, at a space d = 8 cm apart. The capacitor is connected to an electromotive force of 15V.

What is the magnitude of the electric field E between the plates?

(a)   E = 1.2 V/m
(b)   E = 1.9 V/m
(c)   E = 187.5 V/m

### QUESTION 12***

What is the charge of the sphere q, knowing that it is at rest?

(a)   q = -20.9 mC
(b)   q = -20.9 μC
(c)   q = 0 C
(d)   q = 20.9 μC
(e)   q = 20.9 mC

### QUESTION 13***

The plates are now taken to a larger distance of 2d. Which way will the sphere start moving if the plates were displaced while connected to the source?

(a)   down
(b)   up
(c)   will not move

### QUESTION 14**

This and the next two questions pertain to the following situation:

Two identical capacitors are each built from square plates, each of side a. The distance between the capacitor plates is d. Between them is a medium with dielectric constant κ.

Plate 1 is connected to the positive terminal of a battery of Voltage V, while plate 4 is connected to the negative terminal (see figure).

What is the capacitance C of the system?

(a)   C = κ ε0a2 / 2d
(b)   C = κ ε0a2 / d
(c)   C = 2 κ ε0a2 / d

### QUESTION 15**

What is the electrostatic energy U stored in the capacitors?

(a)   U = κ ε0 a2V2/ 4d
(b)   U = κ ε0 a2V2/ 2d
(c)   U = κ ε0 a2V2/ d

### QUESTION 16**

What is the charge q2 on plate 2?

(a)   q2 = - V κ ε0 a2 / 2d
(b)   q2 = 0
(c)   q2 = V κ ε0 a2 / 2d

### QUESTION 17*

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

Compare I3, the current through resistor 3, with I4, the current through resistor 4.

(a)   I3 > I4
(b)   I3 = I4
(c)   I3 < I4

### QUESTION 18***

Compare V1, the voltage across resistor 1, with V5, the voltage across resistor 5.

(a)   V1 > V5
(b)   V1 = V5
(c)   V1 < V5

### QUESTION 19*

How much power is being delivered by the battery?

(a)   P = 23.4 W
(b)   P = 37.1 W
(c)   P = 48.8 W
(d)   P = 62.7 W
(e)   P = 132 W

### QUESTION 20**

What is I2, the current through resistor 2?

(a)   I2 = 0.27 A
(b)   I2 = 0.45 A
(c)   I2 = 0.94 A
(d)   I2 = 1.32 A
(e)   I2 = 3.17 A

### QUESTION 21*

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

Capacitors C1 and C3 relative to each other are

(a)   in parallel.
(b)   in series.
(c)   neither in series nor in parallel.

### QUESTION 22**

Compare V2 the potential across capacitor 2 with V4 the potential across capacitor 4.

(a)   |V2| > |V4|
(b)   |V2| = |V4|
(c)   |V2| < |V4|

### QUESTION 23*

Calculate U, the total energy stored by all of the capacitors in the circuit.

(a)   U = 93 μJ
(b)   U = 124 μJ
(c)   U = 215 μJ
(d)   U = 328 μJ
(e)   U = 583 μJ

### QUESTION 24**

Calculate the charge Q1, on the positive plate of capacitor C1.

(a)   Q1 = 29.2 μC
(b)   Q1 = 41.4 μC
(c)   Q1 = 52.4 μC
(d)   Q1 = 61.0 μC
(e)   Q1 = 73.8 μC

### QUESTION 25***

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

In the circuit shown, the switch has been open for a long time so that the capacitor is uncharged.

What is the current through the battery immediately after the switch is closed?

(a)   I(0+) = 2V/R
(b)   I(0+) = V/(2R)
(c)   I(0+) = V/R

### QUESTION 26***

Which plot shows the current through the right resistor as a function of time starting just after the switch is closed?

(a)
(b)
(c)

### QUESTION 27***

What is the charge on the capacitor after the switch has been closed for a long time?

(a)   Q(∞) = CV/2
(b)   Q(∞) = CV
(c)   Q(∞) = 2CV

### QUESTION 28**

After being closed for a long time, the switch is opened. At what time t after the switch is opened does the charge on the capacitor decrease to e-1 [i.e., (2.718)-1] of the charge that it had just before the switch is opened?

(a)   t = RC/2
(b)   t = RC
(c)   t = 2RC

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.