Five charges +q, +5q, -2q, +3q and -4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is:
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Remember Gauss's Law: The total electric flux through a closed surface is proportional to the net electric charge enclosed within the surface. Charges outside the surface do not contribute to the net flux through the surface.
Gauss's law states that the electric flux \( \phi \) through a closed surface is \( \phi = \frac{q}{\epsilon_0} \). In this formula, \( q \) represents the net charge enclosed by the surface, and \( \epsilon_0 \) is the permittivity of free space. When multiple charges are present within the surface, their individual charges are summed to find the total charge. The charges provided are \( q \), \( -2q \), and \( 5q \). The total charge \( q_{{total}} \) enclosed is calculated as:
\[
q_{{total}} = q + (-2q) + 5q = 4q
\]
Consequently, the electric flux is determined by:
\[
\phi = \frac{q_{{total}}}{\epsilon_0} = \frac{4q}{\epsilon_0}
\]
The electric flux \( \phi \) passing through the closed surface is therefore \( \frac{4q}{\epsilon_0} \).
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