A uniform vertical field is established in the space between two large parallel plates. A small conducting sphere of mass m is suspended in the field from a string of length L. We have to find the period of this pendulum when the sphere is given a charge if the lower plate (a) is charged positively and (b) if it is charged negatively.

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If the lower plate is charged positively, the direction of the electric field will be vertically up and the net force acting downward on the conducting ball of mass m with charge on it will be

.

As the ball is suspended from a string of length L, it will be driven by the tension in the string and for small angular displacements from the vertical the equation of motion will be

It is a simple harmonic motion equation. Its period will be

.

(b)

If the lower plate is charged negatively, the direction of the electric field will be vertically down and the net force acting downward on the conducting ball of mass m with charge on it will be

.

The period of simple harmonic motion of the oscillations in this case will be

.