Three charges -q₁, +q₂ and -q₃ are placed as shown in the figure. The x -component of the force on -q₁ is proportional to (a) (q₂)/(b²) - (q₃)/(a²)cos θ (b) (q₂)/(b²) + (q₃)/(a²)sin θ (c) (q₂)/(b²) + (q₃)/(a²)cos θ (d) (q₂)/(b²) - (q₃)/(a²)sin θ

Answer: (b). +q₂ on the x-axis at distance b attracts -q₁: force (kq₁q₂)/(b²) along +x. -q₃ at distance a along a line making θ with the y-axis (upper left) repels -q₁ towards the lower right. x-component of this repulsion = (kq₁q₃)/(a²)sin θ, also along +x. Fx ∝ (q₂)/(b²) + (q₃)/(a²)sin θ. So the answer is (b).

Three charges -q₁, +q₂ and -q₃ are placed as shown in the figure. The… | JEE Main 2003 (AIEEE)

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Electric Charge & Coulomb's Law

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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Answer: (b)

$+q_2$ on the x-axis at distance $b$ attracts $-q_1$ : force $\dfrac{kq_1q_2}{b^2}$ along $+x$ .
$-q_3$ at distance $a$ along a line making $\theta$ with the y-axis (upper left) repels $-q_1$ towards the lower right.
x-component of this repulsion $= \dfrac{kq_1q_3}{a^2}\sin\theta$ , also along $+x$ .
$F_x \propto \dfrac{q_2}{b^2} + \dfrac{q_3}{a^2}\sin\theta$ . So the answer is (b).

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