Question

Twelve equal charges $\left(q\right)$, are situated at the corners of a regular $12-$sided polygon $($for instance, one on each numeral of a clock face$)$. What is the net force on a test charge $Q$ at the centre?
$($Assume the distance between $q$ and $Q$ pair(s) to be $L)$

• A. $\frac{Qq}{4\pi {ϵ}_o{L}^2}$
• B. $\frac{Qq}{2\pi {ϵ}_o{L}^2}$
• C. $\frac{Qq}{3\pi {ϵ}_o{L}^2}$
• D. Zero

Answer 1

The correct option is D Zero


As shown, forces due to diametrically opposite charges at the centre on charge $Q$ are equal and opposite. Hence they will cancel each other.
Thus, due to all charges net force at the centre on charge $Q$ is zero.