Q.
A point charge is surrounded symmetrically by six identical charges at distance $r$ as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge $q$ at the centre is removed at infinity
A) Zero
B) $6q^{2}/4\pi\varepsilon_{0}r$
C) $q^{2}/4\pi\varepsilon_{0}r$
D) $12q^{2}/4\pi\varepsilon_{0}r$
Explanation
(b) Total potential at the centre $V_{c} = \frac{6q}{4\pi\varepsilon_{0}r}$
Required work done $= q = (V_{c} - V_{\infty})$
$= qV_{c} = \frac{6q^{2}}{4\pi\varepsilon_{0}r}\lbrack V_{\infty} = 0\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.