Chapter 16, Problem 24Q

A point charge is surrounded by a spherical gaussian surface of radius r. If the sphere is replaced by a cube of side r, will ${\varphi }_E$ be larger, smaller, or the same? Explain.

To determine

Whether the flux through a cube and the flux through a gaussian spherical surface are equal for the same enclosed charge

Answer to Problem 24Q

Solution:

Electric flux is the same for both cube and spherical surface.

Explanation of Solution

Electric flux through a closed surface depends only on the charge enclosed by the surface.

That is, electric flux ${\varphi }_E=\frac{Q_{enc}}{{\in }_0}$

Where, $Q_{enc}\to$ charge enclosed by the surface

So, the flux through the cube and spherical surface are same because both the surfaces enclose the same charge.