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?

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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 1 year ago

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