Discussion
A point charge q is placed at a corner of a cube of side-length l. The electric flux through one of the cube faces not passing through the charge q is :
Answer: D
The flux is \( \frac{q}{24\epsilon_{0}} \).
A charge at a corner is shared by 8 cubes that together surround it, so by symmetry the given cube receives \( \frac{q}{8\epsilon_{0}} \) in total. The three faces that meet at the corner contain the charge in their planes, so the field lies along them and their flux is zero. The other three faces share the flux equally:
\[ \begin{aligned} \Phi &= \frac{1}{3} \times \frac{q}{8\epsilon_{0}} \\ &= \frac{q}{24\epsilon_{0}} \end{aligned} \]
\( \frac{q}{6\epsilon_{0}} \) is the flux through one face when the charge is at the centre of the cube, and \( \frac{q}{3\epsilon_{0}} \) and \( \frac{ql^{2}}{\epsilon_{0}} \) do not follow from Gauss's law.
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