Electric Flux with Calculus Video Lessons

Concept

# Problem: 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 εo for the permittivity of free space (not the EMF symbol Eo). Part B. What would be the flux Φ1 through a face of the cube if its sides were of length L1? Use εo for the permittivity of free space.

###### FREE Expert Solution

Electric flux:

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

Part A

A cube has 6 faces with equal area.

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

###### Problem Details

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

Part A. What is the electric flux through each of the six faces of the cube? Use εo for the permittivity of free space (not the EMF symbol Eo).

Part B. What would be the flux Φ1 through a face of the cube if its sides were of length L1? Use εo for the permittivity of free space.