Question

If a charge of 3 nC is placed at each vertex of a cube of side 3 m, then the electric potential at the centre of the cube is:

• A. 48 V
• B. 36 V
• C. 6\(\sqrt{2}\) V
• D. 12\(\sqrt{6}\) V

Hint:

Use symmetry: all vertices contribute equally to potential.
Distance from center to any vertex: $r = \frac{\sqrt{3}}{2}a$.
Total potential = sum of individual potentials.

Answer 1

The Correct Option is C

• Electric potential at the centre due to one point charge $V = \dfrac{kq}{r}$.
• Distance from cube centre to vertex: $r = \frac{\sqrt{3}}{2}a$, $a = 3\ \text{m} \Rightarrow r = \frac{\sqrt{3}}{2}\cdot3 = \frac{3\sqrt{3}}{2}$.
• Potential at center due to 8 vertices: $V = 8 \cdot \dfrac{kq}{r} = 8 \cdot \dfrac{9\times10^9 \cdot 3\times10^{-9}}{3\sqrt{3}/2} = 6\sqrt{2}\ \text{V}$.
• Hence, correct answer: 6$\sqrt{2$ V}.