Question

A cubical Gaussian surface with faces parallel to the Cartesian axes is shown. It's dimensions are 2m on each edge. A uniform electric field (+5 N/C)i + (-7 N/C)j + (-9 N/C)k exists in this region.

a. What is the electric flux through the top face of this cube?

b. How much charge is enclosed inside the cube?

Answer 1

(a) Flux through top surface ADFG ,

..............(1)

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(b) Enclosed charge Q inside the cube is determined by Gauss law as given below

where the integration is closed suface integration perfomed over the surfaces of cube to get the total flux over the enclosed surface. Constant is the permittivity of free space

Flux through front surface ABCD ,

Flux through back surface OEFG ,

Flux through left surface ABOG ,

Flux through left surface CDFE ,

Flux through bottom surface BCEO ,

Hence the toal flux over the surfaces of cube is given as

Since total flux over the surfaces of cube is zero , net enclosed charge also zero