### Fall 2000 Physics 102 Hour Exam 1(31 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 ***.

This exam consists of 31 questions; 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 143. When the exam was given, the mean was 96.8; the median was 98. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

Three charges of equal magnitude are positioned as shown at right, with Q3 equidistant from Q1 and Q2. Q1 and Q3 are positive charges; Q2 is negative. What direction is the force on charge Q3?

(a)   left
(b)   right
(c)   up
(d)   down
(e)   the force is zero

### QUESTION 2*

A positive charge is located near a large conducting plate with a negative charge. Which picture best describes the electric field lines for this system?

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

### QUESTION 3**

Consider a regular pyramid with sides of length d and charge Q fixed on each corner. The (external) work required to build this charge configuration by bringing charges from infinitely far away is:

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

### QUESTION 4**

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

Four charges are fixed at the corners of a square of sides 4m as shown.

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

(a)   -92.6 N-m/C
(b)   -38.2 N-m/C
(c)   0 N-m/C
(d)   +38.2 N-m/C
(e)   +92.6 N-m/C

### QUESTION 5**

What is the magnitude of the electric field at the center of the square?

(a)   13.9 N/C
(b)   27.0 N/C
(c)   37.3 N/C
(d)   55.1 N/C
(e)   84.0 N/C

### QUESTION 6*

What is the direction of the force on charge Q1 due to charges Q2, Q3, and Q4?

(a)   along the vertical
(b)   along the horizontal
(c)   along the diagonal

### QUESTION 7***

What is the magnitude of the force on charge Q1 due to charges Q2, Q3, and Q4?

(a)   1.68 × 10-8 N
(b)   2.37 × 10-8 N
(c)   4.74 × 10-8 N
(d)   7.70 × 10-8 N
(e)   9.78 × 10-8 N

### QUESTION 8***

This and the next question are about the following situation:

Two small spheres with equal unknown mass are suspended by light-weight strings of length 10 cm. When a charge of +5 nC is placed on each sphere, each string makes an angle of 20° with the vertical in equilibrium.

What is the mass of each ball?

(a)   1.21 × 10-6 kg
(b)   3.56 × 10-6 kg
(c)   1.07 × 10-5 kg
(d)   1.35 × 10-5 kg
(e)   2.23 × 10-5 kg

### QUESTION 9**

If an electric field pointing up is applied to the charges, the angle between the strings will

(a)   increase.
(b)   decrease.
(c)   remain the same.

### QUESTION 10*

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

A small particle with charge +15e (e = 1.6 x 10-19 C) is located at the origin, a distance of 5 nm from a second particle of charge –30e.

What is the potential energy of the two-charge system?

(a)   -6.90 × 10-9 J
(b)   -8.98 × 10-12 J
(c)   -3.33 × 10-15 J
(d)   -2.07 × 10-17 J
(e)   -4.15 × 10-19 J

### QUESTION 11***

At what distance d from the +15e particle along the y-axis is the electric potential equal to zero?

(a)   2.50 nm
(b)   2.89 nm
(c)   3.71 nm
(d)   7.35 nm
(e)   10.00 nm

### QUESTION 12***

A third particle of charge –5e is placed on the x-axis at the location –5 nm.

How much work is required to move this particle to the position +10 nm on the x-axis?

(a)   0 J
(b)   6.65 × 10-19 J
(c)   9.56 × 10-19 J
(d)   1.24 × 10-18 J
(e)   5.18 × 10-18 J

### QUESTION 13*

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

Four capacitors are connected as shown. A 15 V battery is centered in the circuit. Assume that all of the capacitors are fully charged and that no current is flowing.

What is the charge on one of the plates of the 4mF capacitor?

(a)   Q4 = 15 mC
(b)   Q4 = 30 mC
(c)   Q4 = 60 mC

### QUESTION 14*

Compute the total stored energy in the capacitors.

(a)   Utot = 0.054 × 10-3 J
(b)   Utot = 0.420 × 10-3 J
(c)   Utot = 0.875 × 10-3 J
(d)   Utot = 1.125 × 10-3 J
(e)   Utot = 2.660 × 10-3 J

### QUESTION 15**

If you place a dielectric with k = 7.5 between the plates of the 1mF capacitor (at the top), the charge on the other three (unmodified) capacitors would

(a)   increase.
(b)   decrease.
(c)   remain the same

### QUESTION 16*

Compute the equivalent capacitance between the points A and B of the following network of capacitors.

(a)   Ceq = C0 / 4
(b)   Ceq = C0 / 2
(c)   Ceq = C0
(d)   Ceq = 2C0
(e)   Ceq = 5C0

### QUESTION 17*

This and the next question are about the following situation:

An isolated parallel-plate capacitor has area A = 3.0 ´ 10-4 m2 and plate separation d = 2 ´ 10-5 m. The charge on each plate has magnitude Q = 11 nC. The capacitor is initially filled with air (k = 1).

Compute the energy stored in the capacitor.

(a)   U = 2.31 × 10-8 J
(b)   U = 4.32 × 10-8 J
(c)   U = 9.06 × 10-8 J
(d)   U = 1.51 × 10-7 J
(e)   U = 4.56 × 10-7 J

### QUESTION 18**

Now a dielectric with k = 7.5 is inserted between the plates (the capacitor remains in isolation from any external circuit). The stored energy will

(a)   increase.
(b)   decrease.
(c)   remain the same.

### QUESTION 19*

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

A single charge of unknown sign and magnitude is located at the origin. A graph of the electrical potential a distance r away from this charge is shown below. We assume that the potential at infinity is zero. The graph is accurately prepared so you can read meaningful values from scales on the axes.

The sign of the charge is

(a)   positive.
(b)   negative.

### QUESTION 20*

The magnitude of the charge is:

(a)   | Q | = 0.22 nC
(b)   | Q | = 5.55 nC
(c)   | Q | = 50.0 nC

### QUESTION 21**

If you moved a -3 nC charge from an initial radius of r = 1 m to a final radius of r = 0.5 m, how much work must you do?

(a)   W = 0.15 µJ
(b)   W = 0.80 µJ
(c)   W = 1.33 µJ
(d)   W = 8.66 µJ
(e)   W = 25.0 µJ

### QUESTION 22*

Which one of the following is a valid Kirchhoff voltage equation for the dotted outside loop?

(a)   +E1 - I1R1 - I3R3 - E3 = 0
(b)   +E1 + I1R1 - I3R3 + E3 = 0
(c)   +E1 - I1R1 + I3R3 - E3 = 0

### QUESTION 23*

Which of the following is a valid Kirchhoff current equation for the above circuit.

(a)   I1 - I2 + I3 = 0
(b)   I1 - I2 - I3 = 0
(c)   I1 + I2 + I3 = 0

### QUESTION 24*

This and the next three questions are about this circuit:

Compare I2, the current through R2, with I3, the current through R3.

(a)   I2 > I3
(b)   I2 = I3
(c)   I2 < I3

### QUESTION 25**

Compare V3, the voltage across R3, with V4, the voltage across R4.

(a)   V3 > V4
(b)   V3 = V4
(c)   V3 < V4

### QUESTION 26*

How much power is being delivered by the battery?

(a)   P = 1.95 W
(b)   P = 5.32 W
(c)   P = 11.9 W
(d)   P = 25.8 W
(e)   P = 28.8 W

### QUESTION 27**

What is I2, the current through R2?

(a)   I2 = 0.248 A
(b)   I2 = 0.387 A
(c)   I2 = 0.459 A
(d)   I2 = 0.521 A
(e)   I2 = 0.692 A

### QUESTION 28**

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

In this circuit, 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+) = 0
(b)   I(0+) = V / R
(c)   I(0+) = 2 V / R

### QUESTION 29**

What is the current through the battery after the switch has been closed a long time?

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

### QUESTION 30*

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

(a)   Q(¥) = C V / 2
(b)   Q(¥) = C V
(c)   Q(¥) = 2 C V

### QUESTION 31***

After being closed for a long time, the switch is opened. How long does it take before the charge on the capacitor drops to 1/2 of the charge it has when the switch is opened? Assume that V = 50 V, C = 4 mF, and R = 10 W.

(a)   t = 13.8 µs
(b)   t = 41.3 µs
(c)   t = 55.5 µs
(d)   t = 88.1 µs
(e)   t = 113.2 µs

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.