A ring of radius 4.0 cm is in the z = 0 plane and has its center at the origin.

Question

A ring of radius 4.0 cm is in the z = 0 plane and has its center at the origin. The ring has a uniform charge of 8.0 nC. Find:

a. the electric field at z = 3.0 cm.

b. the electric potential at z = 3.0 cm.

c. A small particle that has a mass equal to 6.0 mg and a charge equal to 5.0 nC is placed on the z axis at z = 3.0 cm and released. What is the potential energy of the small particle at z = 3.0 cm?

d. Find the speed of the particle when it is a great distance from the ring. Assume effects due to gravity are negligible (1.6 m/s).

Explanation / Answer

k = 9 x 109 Nm2/C2

a = 4 cm = 0.04 m, Q = 8 nC = 8 x 10-9 C, z = 3 cm = 0.03 m, m = 6 mg = 6 x 10-6 kg, q = 5 x 10-9 C

a) field, E = kQz/(z2 + a2)1.5 => E = 17280 N/C

b) potential, V = kQ/(z2 + a2)0.5 => V = 1440 V

c) potential energy = qV = 7.2 x 10-6 J

d) speed = sqrt(2 x energy/m) = 1.5492 m/s

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