Question

At time ( t ), a solid conducting sphere is given a total charge ( q ) that is uniformly spread throughout its volume. Two students discuss whether or not this charge distribution is stable.

a) Stable

b) Unstable

c) Depends on the size of the sphere

d) Depends on the charge magnitude

Answer 1

A charge distribution uniformly spread throughout the volume of a solid conducting sphere is unstable because the charges will move to the surface due to electrostatic forces.

Step-by-step explanation:

The question pertains to the stability of a charge distribution in a solid conducting sphere when uniformly spread throughout its volume. In electrostatics, a conductor in equilibrium will have charges residing on its surface, not within its volume. Therefore, this scenario, though hypothetical, would be an unstable configuration.

Realistically, any excess charge placed within a conductor will move to the surface, making the inner charge density zero and causing the surface to have a uniform charge density. This is due to the electrostatic repulsion between charges and the principle of charge relaxation in conductors. Hence, the correct answer here would be (b) Unstable, since a uniform volume distribution of charge in a conductor cannot be sustained.