Electric flux:

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

**Part A**

A cube has 6 faces with equal area.

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

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

Part A. What is the electric flux through each of the six faces of the cube? Use ε_{o} for the permittivity of free space (not the EMF symbol E_{o}).

Part B. What would be the flux Φ_{1} through a face of the cube if its sides were of length L_{1}? Use ε_{o} for the permittivity of free space.

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