Question

A point charge of magnitude q is at the center of a cube with sides of length L

Part A)

What is the electric flux ? through each of the six faces of the cube?

Use ?0 for the permittivity of free space.

Part B)

What would be the flux ?1 through a face of the cube if its sides were of length L1 ?

Use ?0 for the permittivity of free space.

Answer 1

Gauss law states thatthe electric flux through a closed surface is equal to ^ times the charge enclosed by the surface. Thus, the total flux is ree Therefore, the flux though each face is, 6 68 Since flux is independent ofthe length of each face ofthe cube, even though the length is changed theux remain constamtand is

Answer 2

Electric flux is given by:

$\phi=\frac{q}{\varepsilon _o}$

Part A

$\Rightarrow \phi=\frac{q}{\varepsilon _o}$

this is the total flux through the cube

since a cube has six sides therefore flux through each face is given by:

$\Rightarrow \phi_s=\frac{\phi}{6}=\frac{q}{6\varepsilon _o}$

$\Rightarrow \phi_s=\frac{q}{6\varepsilon _o}$

Part B

if its sides were of length L1 then also the magnitude of the flux will remain same as total charge enclosed is same

therefore now flux is given by

$\Rightarrow \phi_s=\frac{q}{6\varepsilon _o}$