Question

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 \({\phi _{\rm{E}}}\) be larger, smaller, or the same? Explain.

Short answer

The electric flux \({\phi _{\rm{E}}}\) will be the same.

Step-by-step solution

Concepts used in the solution

The electric flux through any closed surface is\({\phi _{\rm{E}}} = \frac{Q}{{{\varepsilon _ \circ }}}\).

The electric flux depends on the charge inside the enclosed surface, not on the shape of the surface.

Explanation for the solution

You know the electric flux does not depend on the shape of the surface. So as the charge is the same inside both closed characters, then the change is the same.