Three charges – q₁, +q₂ and –q₃ are placed as shown in the figure. The x-component of the force on –q₁ is proportional to

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$\frac{q_{2}}{b^{2}} - \frac{q_{2}}{a^{2}} \sin θ$

$\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ$

$\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ$

$\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ$

answer is B.

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Detailed Solution

The x-component of total force on –q₁ is

$F_{x} \propto \frac{q_{1} q_{2}}{b^{2}} + \frac{q_{3} q_{1} \sin θ}{a^{2}} \Rightarrow F_{x} \propto \frac{q_{2}}{b^{2}} + \frac{q_{3} \sin θ}{a^{2}}$

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