Electric flux:

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int}}{\mathbf{E}}{\mathbf{\xb7}}{\mathbf{d}}{\mathbf{s}}{\mathbf{=}}\frac{\mathbf{q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

**(A)**

$\begin{array}{rcl}\mathbf{\int}\mathbf{E}\mathbf{\xb7}\mathbf{d}\mathbf{s}& \mathbf{=}& \frac{\mathbf{q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}\\ \mathbf{E}\mathbf{(}{\mathbf{A}}_{\mathbf{1}}\mathbf{+}{\mathbf{A}}_{\mathbf{2}}\mathbf{+}{\mathbf{A}}_{\mathbf{3}}\mathbf{+}{\mathbf{A}}_{\mathbf{4}}\mathbf{+}{\mathbf{A}}_{\mathbf{5}}\mathbf{+}{\mathbf{A}}_{\mathbf{6}}\mathbf{)}& \mathbf{=}& \frac{\mathbf{q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}\end{array}$

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 *= 2*m? *Use *ε*_{0} 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 *= 5*m**?*

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