Each corner of a cube of side l has a negative charge, −q. The electrostatic potential energy of a charge q at the centre of the cube is ?

Each corner of a cube of side l has a negative charge, −q. The electrostatic potential energy of a charge q at the centre of the cube is ?

(a) \( -\frac{4q^2}{\sqrt{2\pi \varepsilon_0 l}} \)

(b) \( \frac{\sqrt{3} q^2}{4\pi \varepsilon_0 l} \)

(c) \( \frac{4q^2}{\sqrt{2\pi \varepsilon_0 l}} \)

(d) \( -\frac{4q^2}{\sqrt{3\pi \varepsilon_0 l}} \)

Answer :  (d) \( -\frac{4q^2}{\sqrt{3\pi \varepsilon_0 l}} \)

\( U = \frac{-q^2}{4 \pi \varepsilon_0 \sqrt{3} L} \cdot 2 \times 8 \)

\( V = \frac{U}{q} \quad \quad E = \frac{F}{q} \)

\( V = \frac{U}{m} \quad \quad g = \frac{F}{m} \)

\( r = \sqrt{ \left( \frac{L}{2} \right)^2 + \left( \frac{L}{2} \right)^2 + \left( \frac{L}{2} \right)^2 } \)

\( = \sqrt{3} \cdot \frac{L}{2} \)