Question

A point charge is placed at the center of a spherical Gaussian surface. Is changed (a) if the surface is replaced by a cube of the same volume? (b) if the sphere is replaced by a cube of one-tenth the volume? (c) if the charge is moved off center in the original sphere, still remaining inside? (d) if the charge is moved just outside the original sphere? (e) if a second charge is placed near, and outside, the original sphere? (f) if a second charge is placed inside the Gaussian surface?

Answer 1

Explanation:

Electric flux in enclosed surface depends on the total charge inside the surface

It is independent of shape of the Gaussian surface as well as it is independent of position of charge inside the surface

so we have

(a) if the surface is replaced by a cube of the same volume?

No change in the flux as net charge inside the Gaussian surface remains unchanged

(b) if the sphere is replaced by a cube of one-tenth the volume?

No change in the flux as net charge inside the Gaussian surface remains unchanged

(c) if the charge is moved off center in the original sphere, still remaining inside?

No change in the flux as net charge inside the Gaussian surface remains unchanged

(d) if the charge is moved just outside the original sphere?

Flux will change to ZERO because there is no charge inside the surface

(e) if a second charge is placed near, and outside, the original sphere?

No change in flux as the second charge is outside the surface

(f) if a second charge is placed inside the Gaussian surface?

Flux will change as net charge inside the surface will change