Question

$12$ positive charges each of magnitude q are placed on a circle of radius $R$ in a manner such that they are equally spaced. A charge $+Q$ is placed at the centre. If one of the charges q is removed, then the force on $Q$ is :

• A. zero
• B. $\frac{qQ}{4\pi {ϵ}_0{R}^2}$ away from the position of the removed charge
• C. $\frac{11qQ}{4\pi {ϵ}_0{R}^2}$ away from the position of the removed charge
• D. $\frac{qQ}{4\pi {ϵ}_0{R}^2}$ towards the position of the removed charge

Answer 1

The correct option is D $\frac{qQ}{4\pi {ϵ}_0{R}^2}$ towards the position of the removed charge

Answer is D.
$Q$ provides the centripetal force required for $q$ to move in a uniform circular motion. The magnitude of the force is given as $F=\frac{qQ}{4\pi {\epsilon }_0{R}^2}$.
Therefore, If one charge is removed then net force on Q is $\frac{qQ}{4\pi {\epsilon }_0{R}^2}$ towards the position of removed charge as it is positive.