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 ε_{0} 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:

Q_{enc} = q_{1} + q_{5} = 2q

q_{1} = 2q - q_{5} ........(a)

Five charges are arranged as shown. The figure shows five Gaussian surfaces and the electric flux through each. What are the five charges q_{1} to q_{5} in terms of q?

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