Gauss' Law Video Lessons

Concept

# Problem: Five charges are arranged as shown. The figure shows five Gaussian surfaces and the electric flux through each. What are the five charges q1 to q5 in terms of q?

###### FREE Expert Solution

Electric flux:

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{E}}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{enc}}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$, where Q is the electric charge in the given cross-sectional area and ε0 is the permittivity in free space.

From  our figure, $\begin{array}{rcl}{\mathbf{\varphi }}_{\mathbf{A}}& \mathbf{=}& \frac{\mathbf{2}\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}\end{array}$

From the equation of electric flux,

$\begin{array}{rcl}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathbf{\epsilon }}_{\mathbf{0}}}& \mathbf{=}& \frac{\mathbf{2}\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}\\ {\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}& \mathbf{=}& \mathbf{2}\mathbf{q}\end{array}$

The charge enclosed by the Gaussian surface, A is:

Qenc = q1 + q5 = 2q

q1 = 2q - q5 ........(a)

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###### Problem Details

Five charges are arranged as shown. The figure shows five Gaussian surfaces and the electric flux through each. What are the five charges q1 to q5 in terms of q?