A negative charge of -15 µC is placed at the origin. (Assume that all electric p

Question

A negative charge of -15 µC is placed at the origin. (Assume that all electric potentials and potential energies are zero at infinity)
(a) What is the magnitude and direction of the electric field at x = 10 cm?
Magnitude N/C
direction ---Select--- -y -x +x +y
(b) What is the electric potential at x = 10 cm? V
(c) A 5 g mass which carries a charge of -3 µC is placed at x = 10 cm. What is its potential energy? J
(d) If the mass in part (c) is initially at rest and then released, what will its velocity be at infinity (a long distance away)? m/s

Explanation / Answer

a) x = 10 cm

Q = -15 C

Electric Field = - (15 * 10 -6)/4o(10*10-2)2 = 1.34 * 107 N/C in negative x direction

b) Electric Potential = (15 * 10 -6)/4o(10*10-2) = .0134 *10 8 = 1.34 MV

c) Potential energy = 3 * 10-6 * 1.34 * 106 = 4.02 J

d) At infinity potential energy will be zero so apply energy conservation eq.

Total potential energy at x = 10cm = Total kinetic energy at infinity

4.02 = .5 * 5 * 10-3 * V2

V2 = 4.02 / (.5 * 5 * 10 -3) = 16.08 * 102

V = 4.0099 * 10 = 40.099 m/s

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