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Three charges $-q_1,+q_2$ and $-q_3$ are placed as shown in the figure, The x-component of the force on $-q_1$ is proportional to
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$\frac{q_2}{b^2}-\frac{q_3}{a^2}\cos θ$ $\frac{q_2}{b^2}+\frac{q_3}{a^2}\sin θ$ $\frac{q_2}{b^2}+\frac{q_3}{a^2}\cos θ$ $\frac{q_2}{b^2}-\frac{q_3}{a^2}\sin θ$ |
$\frac{q_2}{b^2}+\frac{q_3}{a^2}\sin θ$ |
$\text{Force due to} +q_2\, \text{on}\, -q_1 = \frac{kq_1q_2}{b^2} \text{along +x direction}$ $\text{X component of force on} -q_1\, \text{due to}\, -q_3= \frac{kq_1q_3 sin\theta}{a^2}\text{along + x direction}$ $\text{X component of force} \propto \frac{q_2}{b^2} + \frac{q_3 sin\theta}{a^2}$ |
