Question

A student said, “The electric field inside a uniformly charged sphere is always zero.” Describe a situation where this is not true.

Short answer

The field inside a uniformly charged sphere is not zero at all points except the center of the sphere.

Step-by-step solution

Identification of given data

A uniformly charged sphere.

Field due to a uniformly charged sphere

The electric field inside a uniformly charged sphere with charge Q and radius R at a distance r from the center is

$\mathit{E}\mathbf{=}\frac{\mathbf{Q}\mathbf{r}}{\mathbf{4}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}{\mathbf{R}}^{\mathbf{3}}}$

Here, ${\mathit{\epsilon }}_{\mathbf{0}}$ is the permittivity of free space

Determination of the case where the field inside a charged sphere is not zero

From equation (i), it is evident that the field inside a uniformly charged sphere is zero when

$r=0$

that is at the center of the sphere.

Thus, the field is not zero at all points except the center of the sphere.