Question

A charge $ q $ is placed at the corner of a cube of side $ a $ . The electric flux through the cube is

• A. $ \frac{q}{\varepsilon_{0}} $
• B. $ \frac{q}{3\varepsilon_{0}} $
• C. $ \frac{q}{6\varepsilon_{0}} $
• D. $ \frac{q}{8\varepsilon_{0}} $

Answer 1

Answer: (D)

According to Gauss's law, the electric flux through a closed surface is equal to $ \frac{1}{ \varepsilon_0} $ times the net charge enclosed by the surface. Since, q is the charge enclosed by the surface, then the electric flux $ \phi = \frac{q}{ \varepsilon_0} $
If charge q is placed at a comer of cube, it will be divided into 8 such cubes. Therefore, electric flux through the cube is
$ \phi ' = \frac{ 1}{ 8} \bigg( \frac{q}{ \varepsilon_0} \bigg) $