Question

A regular polygon has $20$ sides. Equal charges, each $Q,$ are placed at $19$ vertices of the polygon and a charge $q$ is placed at the centre of polygon. If the distance of each vertex from the centre is ${}^{\prime }{a}^{\prime },$ net force experienced by $q$ is:-

• A. $\frac{1}{4\pi {ϵ}_0}\frac{20Qq}{a^2}$
• B. $\frac{1}{4\pi {ϵ}_0}\frac{Qq}{a^2}$
• C. $\frac{1}{4\pi {ϵ}_0}\frac{19Qq}{a^2}$
• D. Zero

Answer 1

Answer: (B)

All $18Q$ charges cancel out their forces to each other, then remain one will exert a force;
$F=\frac{KQq}{q^2}$
$=\frac{1}{4\pi {ϵ}_0}\frac{Qq}{a^2}$