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Conceptual Questions (1point each): Circle the BEST answers. 1. An Electron is placed in an electron ‘gun’ and shot out as shown. Circle all that are true. As the electron moves from A to B: a) ∆U > 0 b) ∆U < 0 c) ∆K > 0 d) ∆K < 0 e) Work done on electron > 0 f) Work done on electron< 0

2. The electric field due to an infinite plane with uniform charge density a.

σ . ε0

b.

σ . 2ε 0

c.

σ r2 . 2ε 0 x 2

σ

is given by

x d. 2π kσ 1 − 2 R + x2

(

. 1/ 2 )

e.

σ 2π kr 2 x2

3. A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is a.

−

3keq . r

3)keq . b. − ( l n r

c. d.

keq . r 3k q + e . r +

4. Equipotentials are lines along which a. the electric field is constant in magnitude and direction. b. the electric charge is constant in magnitude and direction. c. maximum work against electrical forces is required to move a charge at constant speed. d. a charge may be moved at constant speed without work against electrical forces. e. charges move by themselves.

5. A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground. The outside of the sphere is then grounded as shown. Then the ground wire is removed. A is the inner surface and B is the outer surface. Which statement is correct?

a. b. c. d. e.

The charge on A is −q; that on B is +q. The charge on B is −q; that on A is +q. The charge is +q./2 on A and on B. There is no charge on either A or B. The charge on A is −q; there is no charge on B.

Short Problems (10 points each): Show your work for any credit. Box final answers. Use three significant figures. Neatness Counts! For each problem, sketch the situation, labeling everything. 1. If Q = 25 µC, q = 10 µC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q? Redraw the diagram and draw a force diagram showing the net forces acting on q.

a. b. c. d. e.

28 N 22 N 20 N 14 N 10 N

2. Two particles, each having a mass of 3.0 µg and having equal but opposite charges of magnitude of 6.0 nC, are released simultaneously from rest when they are a very large distance apart. What distance separates the two at the instant when each has a speed of 5.0 m/s? a. 4.3 m b. 8.6 m c. 7.3 m d. 5.6 m e. 2.2 m

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Long Problems (25 points each): Show your work for any credit. Box final answers. Use three significant figures. Neatness Counts! For each problem, sketch the situation, labeling everything. 1. A charge of is distributed along the y axis from y1= 3.00 m to y2= 5.00 m with a non-uniform charge distribution given by λ = λ0 y . Find a value for the potential at the origin. Sketch the situation, labeling everything and do the integral. Make it neat. Show ALL the work. Q =50.0 nC .

2. A long (infinite) nonconducting cylinder (R = 6.00 mm) has a nonuniform volume charge density given by αr2, where α = 6.20 mC/m5 and r is the distance from the axis of the cylinder. a. Derive an expression for E for r

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