# Problem: A point charge of magnitude q is at the center of a cube with sides of length L.A: What is the electric flux Φ through each of the six faces of the cube if  L = 2m? Use ε0 for the permittivity of free space.B: What would be the flux Φ through a face of the cube if its sides were of length L = 5m?

###### FREE Expert Solution

Electric flux:

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int }}{\mathbf{E}}{\mathbf{·}}{\mathbf{d}}{\mathbf{s}}{\mathbf{=}}\frac{\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$

(A)

$\begin{array}{rcl}\mathbf{\int }\mathbf{E}\mathbf{·}\mathbf{d}\mathbf{s}& \mathbf{=}& \frac{\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}\\ \mathbf{E}\mathbf{\left(}{\mathbf{A}}_{\mathbf{1}}\mathbf{+}{\mathbf{A}}_{\mathbf{2}}\mathbf{+}{\mathbf{A}}_{\mathbf{3}}\mathbf{+}{\mathbf{A}}_{\mathbf{4}}\mathbf{+}{\mathbf{A}}_{\mathbf{5}}\mathbf{+}{\mathbf{A}}_{\mathbf{6}}\mathbf{\right)}& \mathbf{=}& \frac{\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}\end{array}$

###### Problem Details

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

A: What is the electric flux Φ through each of the six faces of the cube if  = 2m? Use ε0 for the permittivity of free space.

B: What would be the flux Φ through a face of the cube if its sides were of length = 5m?