Question 42 of 311

Three charges $+Q,q,+Q$ are placed respectively, at distance, $0,d/2$ and $d$ from the origin, on the $x$ -axis. If the net force experienced by $+Q,$ placed at $x=0,$ is zero, then value of $q$ is:

A$+Q/2$B$+Q/4$C$-Q/4$D$-Q/2$

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Answer: (C) $-Q/4$

For net force on charge placed at origin is given as
$\Rightarrow \dfrac{K{Q.q}^{}}{{\left(\dfrac{d}{2}\right)}^{2}}+\dfrac{K{Q}^{2}}{{d}^{2}}=0$, where $K$ is a constant.
Solving the above equation, we get, $q=\dfrac{-Q}{4}$
Hence, the charge $q=-\dfrac{Q}{4}$ such that net force on the charge $+Q$ placed at origin is zero.