Three charges $q, Q$ and $+4 q$ are placed in a straight line of length $d$ at points at distances $0,…

Three charges $q, Q$ and $+4 q$ are placed in a straight line of length $d$ at points at distances $0, \frac{d}{2}$ and d respectively. In order to make the net force on $q$ to be zero, the value of $Q$ should be
  1. $-2 q$
  2. $\frac{-q}{2}$
  3. $-q$
  4. $\frac{-3}{2} q$

Solution

Consider the diagram below: To make net force on $q$ is zero, charge $Q$ should be negative. $\begin{aligned} & \therefore \frac{k q Q}{\left(\frac{d}{2}\right)^2}+\frac{k q(4 q)}{d^2}=0 \\ & \Rightarrow Q=-q \end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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