A point charge q is located at the center of a cube whose sides are of...

A point charge q is located at the center of a cube whose sides are of length a. If there are no other charges in this system, what is the electric flux through one face of the cube?

Expert Solution

Electric flux linked with any surface is defined as the total number of electric lines of force that normally pass through that surface.

Electric flux is a scalar quantity

Gauss's theorem which states that the surface integral of the electric field intensity over any closed surface

(called gaussian surface) in free space is equal to 1/ ε0 times the net charge enclosed within the surface.

Hence total electric flux over a closed surface in vaccum is 1/ε0 times the total charge within the surface regardless of how the charges may be distributed.

Where ε0 is permittivity of free space.

Electric flux = total charge / ε0

In the given question the total charge is given = q

So electric flux through the cube = q/ε0

Electric flux(total electric field lines) which will be uniformly exit out from all the faces of cube .

A cube has 6 faces.

Then flux from each face = total flux/ 6

So flux = q/( 6.ε0) from each face of cube.

The flux is independent of the length of the cube.

genius_generous answered 2 years ago

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