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Three charges \(4 q, Q\) and \(q\) are placed at positions \(0, \frac{l}{2}\) and \(l\) respectively along a straight line. If the resultant force on \(q\) is zero, then \(Q\) is equal to
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The correct answer is:
\(-q\)
The given arrangement of charges is shown in following figure,
Resultant force on charge \(q\) is zero.
\(\begin{aligned}
& \text {i.e., } K \cdot \frac{4 q \cdot q}{l^2}+\frac{K Q q}{(l / 2)^2}=0 \\
& \Rightarrow \quad \frac{4 q}{l^2}+\frac{4 Q}{l^2}=0 \\
& q+Q=0 \\
& Q=-q \\
\end{aligned}\)
Resultant force on charge \(q\) is zero.
\(\begin{aligned}
& \text {i.e., } K \cdot \frac{4 q \cdot q}{l^2}+\frac{K Q q}{(l / 2)^2}=0 \\
& \Rightarrow \quad \frac{4 q}{l^2}+\frac{4 Q}{l^2}=0 \\
& q+Q=0 \\
& Q=-q \\
\end{aligned}\)
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