### Fall 2010 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 108. The exam period was 90 minutes; the mean score was 79.5; the median was 81. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

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

A solid, infinite metal cylinder of radius a = 1.5 cm is centered on the origin, and has charge density λinner = -5 nC/cm. Surrounding this cylinder is a cylindrical metal shell of inner radius b = 3.0 cm and outer radius c = 4.5 cm. This shell is also centered on the origin, and has total charge density λshell = +2 nC/cm.

If a positive point charge were placed on the x-axis at the location x = 8 cm and released from rest, it would

(a)   move away from the origin.
(b)   move toward the origin.
(c)   remain at rest.

### QUESTION 2*

Find the magnitude |E| of the electric field at a radius of 8 cm from the origin (e.g. at the point (x, y) = (8 cm, 0)).

(a)   |E| = 1.8×104 N/C
(b)   |E| = 3.2×104 N/C
(c)   |E| = 4.6×104 N/C
(d)   |E| = 6.7×104 N/C
(e)   |E| = 1.3×105 N/C

### QUESTION 3**

Find the potential difference Va - Vc between the surface of the metal cylinder (r = a) and the outer surface of the metal shell (r = c).

(a)   Va - Vc = -8.7 kV
(b)   Va - Vc = -6.2 kV
(c)   Va - Vc = 0
(d)   Va - Vc = +6.2 kV
(e)   Va - Vc = +8.7 kV

### QUESTION 4*

What is the linear charge density, λsh,outer on the outer surface of the cylindrical shell?

(a)   λsh,outer = +3 nC/cm
(b)   λsh,outer = 0 nC/cm
(c)   λsh,outer = -3 nC/cm

### QUESTION 5*

What is the surface charge density σinner on the inner solid metallic cylinder which has radius a?

(a)   σinner = 0
(b)   σinner = -0.53 nC/cm2
(c)   σinner = -3.33 nC/cm2

### QUESTION 6**

If the shell is connected to ground, the charge density λsh,inner on the inner surface (with radius b) of the cylindrical shell will

(a)   increase in magnitude.
(b)   be zero.
(c)   remain unchanged.

### QUESTION 7*

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

A solid spherical insulator has radius R = 2.5 cm, and carries a total positive charge Q = 8 × 10-10 C distributed uniformly throughout its volume.

Find the magnitude of the electric field |E| at a radius of 5 cm from the origin (i.e., outside the sphere).

(a)   |E| = 2.88×103 N/C
(b)   |E| = 8.92×103 N/C
(c)   |E| = 2.41×104 N/C
(d)   |E| = 5.01×104 N/C
(e)   |E| = 8.30×104 N/C

### QUESTION 8*

If we define the electric potential V to be zero at the surface of the sphere, what is the potential V at a radius of 5 cm from the origin?

(a)   V = +2500 V
(b)   V = +985 V
(c)   V = -144 V
(d)   V = -2500 V
(e)   V = -3700 V

### QUESTION 9**

Which of the three diagrams shown here best represents the electric potential as a function of r, the distance from the origin?

(a)
(b)
(c)

### QUESTION 10*

This and the next question refer to this situation:

The electric field lines (solid) and the equipotential lines (dashed) in a certain region of space are as shown here.

When a positive charge is moved from point A to point D, the work done by the electric field is

(a)   greater than the work done by the field when the same charge is moved from point B to point C.

(b)   equal to the work done by the field when the same charge is moved from point B to point C.

(c)   less than the work work done by the field when the same charge is moved from point B to point C.

### QUESTION 11***

The electric potential at C is

(a)   greater than the electric potential at B.
(b)   equal to the electric potential at B.
(c)   less than the electric potential at B.

### QUESTION 12*

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

Two charged, thin, metal plates of infinite area are placed in the planes x = -a and x = +a, as shown in the figure. Each plate carries a negative surface charge density σp = -3 μC/m2. Finally, a metal slab of thickness a and infinite area is placed so that its left-hand surface coincides with the plane x = +3a. This metal slab carries a total positive charge density σs = +8 μC/m2.

The potential energy of a positive charge moving from point B to point A will

(a)   decrease.
(b)   remain constant.
(c)   increase.

### QUESTION 13**

Find the magnitude of the electric field at the origin.

(a)   |E| = |σp| / ε0
(b)   |E| = |σs| / ε0
(c)   |E| = |σs| / (2ε0)
(d)   |E| = |σs+2σp| / (2ε0)
(e)   |E| = |σs-2σp| / (2ε0)

### QUESTION 14**

Find the surface-charge density σR on the right-hand surface of the metal slab (the plane containing point C).

(a)   σR = σs / 2
(b)   σR = 2σp
(c)   σR = (σs + σp) / 2
(d)   σR = (σs/2) + σp
(e)   σR = 0

### QUESTION 15**

An uncharged metal sphere will

(a)   be repelled by a charged metal surface.
(b)   feel no force when brought close to a charged metal surface.
(c)   be attracted by a charged metal surface.

### QUESTION 16**

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

A positive point charge q = +3 μC is placed on the y axis at y = +5 cm. A negative point charge -q = -3 μC is placed at the origin.

At how many points on the y axis could an additional positive charge +q be placed without changing the potential energy of the system?

(a)   no points
(b)   1 point
(c)   2 points

### QUESTION 17*

Calculate the work done by the field to bring in an additional point charge +q from infinity to the point A. (The other two charges are held in position during this procedure.)

(a)   W = 2.98 J
(b)   W = 0.47 J
(c)   W = 0 J
(d)   W = -1.36 J
(e)   W = -5.19 J

### QUESTION 18**

What is the potential energy U of the square arrangement of charges at right?

(a)   U > 0
(b)   U = 0
(c)   U < 0

### QUESTION 19*

This and the next three questions are related.

The circuit at left contains 3 capacitors, all of initial value C = 3 μF.

What is the charge Q1 on capacitor C1?

(a)   Q1 = 18.3 μC
(b)   Q1 = 21.4 μC
(c)   Q1 = 27 μC
(d)   Q1 = 30.8 μC
(e)   Q1 = 33.7 μC

### QUESTION 20*

What is the charge Q2 on capacitor C2?

(a)   Q2 = 9.1 μC
(b)   Q2 = 13.5 μC
(c)   Q2 = 21.4 μC
(d)   Q2 = 33.7 μC
(e)   Q2 = 42.8 μC

### QUESTION 21**

Now suppose C3 is modified by filling it with a dielectric with constant κ = 3. How does the charge Q2 on C2 change?

(a)   Q2 decreases because the capacitance of C2 decreases relative to that of C3.
(b)   Q2 stays the same because the charge of capacitors in series is the same.
(c)   Q2 increases because the capacitance of C3 increases.

### QUESTION 22*

How does the charge Q1 on C1 change when C3 is modified by filling it with a dielectric with constant κ = 3?

(a)   Q1 decreases because the capacitance of C1 decreases relative to that of C3.
(b)   Q1 stays the same because the voltage across C1 is the same as it was originally.
(c)   Q1 increases because the effective capacitance of the C2 C3 part of the circuit increases.

### QUESTION 23*

This and the next two questions are related.

The X-ray tube shown at right is used to accelerate electrons which hit a target and produce X-rays. The device consists of two parallel, metal plates of very large area separated by a 10 cm gap. The plate on the left ("cathode") is connected to ground, while the plate on the right ("anode") is set to a potential of +11 kV. Electrons are produced (at rest) at the cathode plate. They accelerate across the gap, and strike the target area where they slow down rapidly and produce X-rays.

Calculate the final speed v achieved by electrons of mass m = 9.1 × 10-31 kg and charge magnitude |q| = 1.6 × 10-19 C.

(a)   v = 9.1 × 105 m/s
(b)   v = 7.3 × 106 m/s
(c)   v = 2.3 × 107 m/s
(d)   v = 6.2 × 107 m/s
(e)   v = 4.1 × 108 m/s

### QUESTION 24***

If, when the tube is operating, the surface charge densities on the cathode and anode are equal and opposite, what is their magnitude σ ?

(a)   σ = 0.49 μC/m2
(b)   σ = 0.97 mC/m2
(c)   σ = 1.24 μC/m2
(d)   σ = 1.56 μC/m2
(e)   σ = 1.95 μC/m2

### QUESTION 25**

If the charge densities on the cathode and anode are equal and opposite as above, outside the tube the electric field will point

(a)   to the right on the right side of the tube and to the left on the left side of the tube.
(b)   to the left on the right side of the tube and to the right on the left side of the tube.
(c)   the field will be zero everywhere to the left of the cathode and to the right of the anode.

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.