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 $'a',$ net force experienced by $q$ is:-

• A. $\frac{1}{4 \pi \epsilon _{0}}\frac{20 Q q}{a^{2}}$
• B. $\frac{1}{4 \pi \epsilon _{0}}\frac{Q q}{a^{2}}$
• C. $\frac{1}{4 \pi \epsilon _{0}}\frac{19 Q q}{a^{2}}$
• D. Zero

Answer 1

Answer: (B)

All $18Q$ charges cancel out their forces to each other, then remain one will exert a force;
$F=\frac{K Q q}{q^{2}}$
$=\frac{1}{4 \pi \epsilon _{0}}\frac{Q q}{a^{2}}$