Download Fig. 1: Four charged rods.

Electricity and Magnetism: PHY-204
Fall Semester 2013
Electrostatic potential and energy
1. Two parallel plates having charges of equal magnitude but opposite sign are separated
by 12.0 cm. Each plate has a surface charge density of 36.0 nC/m2 . A proton is
released from rest at the positive plate. Determine
(a) the potential difference between the plates.
(b) the kinetic energy of the proton when it reaches the negative plate.
(c) the speed of the proton just before it strikes the negative plate.
(d) the acceleration of the proton, and
(e) the force on the proton.
From the force find the magnitude of the electric field and show that it is equal to the
electric field found from the charge densities on the plates.
2. Four rods of length ℓ are arranged along the edges of a square. The rods carry charge
+Q uniformly distributed along their lengths (see Fig. 1). Find the potential at the
point P at a distance x from one corner of the square.
Fig. 1: Four charged rods.
3. A particle with charge q is located at x = −R, and a particle with charge −2q is
located at the origin. Prove that the equipotential surface that has zero potential is a
sphere centered at (−4R/3, 0, 0) and having a radius r = 2R/3.
4. Four balls, each with mass m, are connected by four nonconducting strings to form
a square with side a as shown in Fig. 2. The assembly is placed on a horizontal,
Date: 13 September, 2013
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Electricity and Magnetism: PHY-204
Fall Semester 2013
nonconducting, frictionless surface. Balls 1 and 2 each have charge q, and balls 3 and
4 are uncharged. Find the maximum speed of balls 3 and 4 after the string connecting
balls 1 and 2 is cut.
Fig. 2
5. Four positive and four negative point charges of equal magnitudes ±Q are arranged
alternately on the corners of a cube of edge d (see Fig. 3). What is the electric energy
of this arrangement.
Fig. 3: Point charges at the corner of a cube.
Date: 13 September, 2013
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