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 60.5; the median was 59. Click here to see page1 page2 of the formula sheet that came with the exam.

Four equally massive charges are held in place equidistant from the origin on the x and y axes as shown in the figure. The charges on the x-axis are positive (+Q) and the charges on the y-axis are negative (-Q). When the charges are simultaneously released they

(a) all are drawn to the origin where they collide. (b) all are repelled outward away from the origin. (c) remain fixed at their initial positions because they each experience no net force.

Two charges are placed on the x-axis as shown in the figure. A charge of -Q is placed at the origin and a charge of +4Q is placed at x = -a.

Referring to the figure, where on the x-axis is the electric field zero?

(a) at a point to the right of the origin (b) at a point between x = -a and x = 0 (c) at a point to the left of x = -a

The diagram shows electric field lines (solid) and equipotential lines (dashed) for a region of space. The charges giving rise to the electric field and equipotential lines are outside of the illustrated region. The points, A, B, C and D are locations in space that are referred to in these two questions.

The magnitude of the work done by an external agent in moving a positive test charge from point C to point D is

(a) less than the magnitude of the work done to move the same positive charge from point A to point B. (b) more than the magnitude of the work done to move the same positive charge from point A to point B. (c) equal to the magnitude of the work done to move the same positive charge from point A to point B.

(T) True (F) False

The electric field at the orgin is

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

Which one of the above graphs best represents the magnitude of the electric potential as a function of radial distance from the center of the shell?

(a) (b) (c)

Charged capacitor C_{1} is now connected to uncharged capacitor C_{2} as shown. Which statement below is valid about the voltage V_{1} across capacitor C_{1} after being connected to capacitor C_{2}?

(a) (1/3) Q (b) (1/7) Q (c) (1/5) Q (d) (3/14) Q (e) (5/7) Q

An infinite conducting metal plate with thickness T is parallel to an infinite sheet of charge with a surface charge density σ. The distance between the center of the metal plate and sheet of charge is d. The field between the sheet of charge and the metal plate is E = E_{L}x and the field to the right of the metal plate is E = E_{R}x. Assume that E_{R} > 0 and E_{R} > 0, as shown in the figure; E_{L} and E_{R} may not be equal in magnitude. The surface charge density on the left and right surfaces of the metal plate are denoted σ_{L} and σ_{R} respectively. No other charges are present. It is not known if there is a net charge on the conducting plate.

Which one of these expressions correctly describes the voltage difference ΔV = V_{sheet} - V_{plate}?

(a) σ_{L} and σ_{R} are of the opposite sign. (b) σ_{L} and σ_{R} are of the same sign. (c) σ_{L} and σ_{R} are always equal.

(a) σ = ε_{0}(E_{R}-E_{L}) / 2 (b) σ = -2ε_{0}(E_{R}+E_{L}) (c) σ = ε_{0}(E_{R}+E_{L}) (d) σ = 2ε_{0}(E_{R}+E_{L}) (e) σ = ε_{0}(E_{L}-E_{R}) / 2

The figure shows a cross-sectional view of two concentric, infinite length, conducting cylindrical shells. The inner shell has as an inner radius of a and an outer radius of b. The electric field just outside the inner shell has magnitude E_{0} and points radially outward as shown. The grounded, outer shell has an inner radius c and an outer radius of d.

Some of the cylindrical surfaces may be charged. Let σ_{a}, σ_{b}, σ_{c} and σ_{d} be the surface charge densities on the surfaces with radii a, b, c and d. There are no other charges or conductors in the problem.

The surface charge density σ_{a} is zero.

(a) |σ_{c}| = |σ_{d}| (b) |σ_{c}| > |σ_{d}| (c) |σ_{c}| < |σ_{d}|

(a) σ_{c} = 2ε_{0}E_{0} (b) σ_{c} = -ε_{0}E_{0} (c) σ_{c} = +ε_{0}E_{0}(c/d) (d) σ_{c} = ε_{0}E_{0} (e) σ_{c} = -ε_{0}E_{0}(b/c)

1) The first capacitor is charged from a battery, disconnected, and then the dielectric is inserted so that it is totally between the plates. 2) The second capacitor remains connected to the same battery and then the dielectric is inserted so that it is totally between the plates.

2) The second capacitor remains connected to the same battery and then the dielectric is inserted so that it is totally between the plates.

After the dielectrics are inserted in both cases:

(a) The energy stored in the first capacitor in case 1) is larger than the energy stored in the second capacitor in case 2). (b) The energy stored in the first capacitor in case 1) is smaller than the energy stored in the second capacitor in case 2). (c) The energy stored in both capacitors is the same.

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

(a) increases, because positive net work was done on q bringing it in from infinity. (b) remains unchanged, because no net work was done on q bringing it in from infinity. (c) decreases, because negative net work was done on q bringing it in from infinity.

Three charges Q_{1}, Q_{2} and Q_{3} are arranged on the y-axis as shown in the figure below. A fourth charge q is brought in from infinity, and placed on the x-axis a distance of a = 1 m from the origin. Q_{1} is located at (0, a), Q_{2} is located at the origin and Q_{3} is located at (0,-a).

Find the energy stored in the charge configuration of Q_{1}, Q_{2} and Q_{3} (the work which was necessary to assemble the three charges in the absence of q).

(a) U = -0.201 J (b) U = -0.0123 J (c) U = 0.00475 J (d) U = 0.0345 J (e) U = 0.0693 J

(a) F_{x} = -0.0378 N (b) F_{x} = -0.0252 N (c) F_{x} = 0.0180 N (d) F_{x} = 0.0334 N (e) F_{x} = 0.0524 N

A negative test charge of mass m and charge -q is placed a distance z above the center of a uniformly, positively charged circular hoop of radius b, with a linear charge density of λ C/m.

Which of these graphs best represents the potential energy U of the negative test charge as a function of z, assuming λ > 0 ?