Question

What is the electric flux φ through each of the six faces of the cube? use ϵ0 for the permittivity of free space (not the emf symbol e0).

Answer 1

Hi there!

Recall the equation for electric flux:

`\Phi _E = \oint E \cdot dA = (Q_(encl))/(\epsilon_0)`

Assuming a charge enclosed by a cube, we know the total electric flux is equal to:

`\Phi_E = (Q_(encl))/(\epsilon_0)`

Since there are 6 faces for a cube, we know that each face has 1/6th of the flux passing through it.

Therefore, the amount of flux going through EACH face is equal to:

`\Phi_E = (1)/(6)(Q_(encl))/(\epsilon_0) = \boxed{(Q_(encl))/(6\epsilon_0)}`