A small conducting sphere of mass and unknown charge hangs from a light
PHYSICS · Multi-part · CBSE · Physics · Electric Charges and Fields · Electric Charges and Fields
Problem
A small conducting sphere of mass m and unknown charge q hangs from a light, inextensible string of length L. The string is fixed to the ceiling. A separate positive point charge Q is mounted at the same height as the ceiling, a horizontal distance D from the point of suspension of the string. In equilibrium the sphere comes to rest so that the string makes an angle θ with the vertical.
Air resistance is negligible, and the only forces on the sphere are gravity, tension, and the electrostatic interaction with Q.
(a) Draw and label a clear free-body diagram for the sphere when it is in equilibrium at the angle θ.
(b) Derive an expression for the magnitude of the sphere’s charge q in terms of m, g, Q, D, and θ.
(c) Determine an expression for the tension T in the string while the sphere is in equilibrium, again in terms of the given quantities.