Q154 / 160 · AP EAMCET 2020 (18 Sep Shift 1) · Physics
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
- Correct answerA\(-q\)
- B\(-2 q\)
- C\(-\frac{q}{2}\)
- D\(4 q t\)
Solution
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. \(\begin{aligned} & \text {i.e., } K \cdot \frac{4 q \cdot q}{l^2}+\frac{K Q q}{(l / 2)^2}=0 \\ & \Rightarrow \quad \frac{4 q}{l^2}+\frac{4 Q}{l^2}=0 \\ & q+Q=0 \\ & Q=-q \\ \end{aligned}\)
Hence, the correct answer is option: 'A'.