Question

A charge Q is situated at the corner A of a cube, the electric flux through the one face of the cube is

• A. $\frac{Q}{6\varepsilon_{0}}$
• B. $\frac{Q}{8\varepsilon_{0}}$
• C. $\frac{Q}{24\varepsilon_{0}}$
• D. $\frac{Q}{2\varepsilon_{0}}$

Answer 1

Answer: (C)

$\frac{Q}{24\varepsilon_{0}}$

Answer 2

For the charge at the corner, we require eight cube to symmetrically enclose it in a Gaussian surface. The total flux $\varphi_{T} = \frac{Q}{\varepsilon_{0}}$. Therefore the flux through one cube will be $\varphi_{cube} = \frac{Q}{8\varepsilon_{0}}.$ The cube has six faces and flux linked with three faces (through A) is zero, so flux linked with remaining three faces will $\frac{\varphi}{8\varepsilon_{0}}.$ Now as the remaining three are identical so flux linked with each of the three faces will be $= \frac{1}{3} \times \left\lbrack \frac{1}{8}\left( \frac{Q}{\varepsilon_{0}} \right) \right\rbrack = \frac{1}{24}\frac{Q}{\varepsilon_{0}}$.