Three point charges Q_1, Q_2 and Q_3 are located in x - y plane at points (- d, 0),(0,0) and ( d, 0) respectively. Q_1 and Q_3 are identical and Q_2…

Nature of \(\displaystyle \mathrm{Q}_{1}\) Value of \(\displaystyle \mathrm{Q}_{1}\) Nature of \(\displaystyle \mathrm{Q}_{1}\) will be negative. Let, \(\displaystyle \mathrm{Q}_{1}=\mathrm{Q}_{3}=\mathrm{q}\) \[\begin{aligned} & \frac{1}{4 \pi \varepsilon_{0}}\left[\frac{\mathrm{q} \mathrm{Q}_{2}}{\mathrm{d}}+\frac{\mathrm{q} \mathrm{q}}{2 \mathrm{d}}+\frac{\mathrm{Q}_{2} \mathrm{q}}{\mathrm{d}}\right]=0 \\ & \frac{1}{4 \pi \varepsilon_{0} \mathrm{d}}\left[\mathrm{q} \mathrm{Q}_{2}+\frac{\mathrm{q}^{2}}{2}+\mathrm{Q}_{2} \mathrm{q}\right]=0 \\ & 2 \mathrm{q} \mathrm{Q}_{2}+\frac{\mathrm{q}^{2}}{2}=0 \\ & 2 \mathrm{q} \mathrm{Q}_{2}=-\frac{\mathrm{q}^{2}}{2} \\ & \mathrm{Q}_{1}=\mathrm{q}=-4 \mathrm{Q}_{2} \end{aligned} \]