SATHEE: Electrostatics 1 Question 7

Electrostatics 1 Question 7

7. Two charges, each equal to $q$ , are kept at $x = - a$ and $x = a$ on the $x$ -axis. A particle of mass $m$ and charge $q_{0} = \frac{q}{2}$ is placed at the origin. If charge $q_{0}$ is given a small displacement $y (y < a)$ along the $y$ -axis, the net force acting on the particle is proportional to

(a) $y$

(b) $- y$

(c) $\frac{1}{y}$

(d) $- \frac{1}{y}$

(2013 Main)

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Answer:

Correct Answer: 7. (b)

Solution:

$\begin{aligned} F_{n e t} & = 2 F \cos θ \\ F_{n e t} & = \frac{2 k q \frac{q}{2}}{{(\sqrt{y^{2} + a^{2}})}^{2}} \cdot \frac{y}{\sqrt{y^{2} + a^{2}}} \\ F_{net} & = \frac{2 k \sin θ}{{(y^{2} + a^{2})}^{3 / 2}} \Rightarrow \frac{k q^{2} y}{a^{3}} \propto y \end{aligned}$

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Electrostatics 1 Question 7

7. Two charges, each equal to q, are kept at x=−a and x=a on the x-axis. A particle of mass m and charge q0=q2 is placed at the origin. If charge q0 is given a small displacement y(y<a) along the y-axis, the net force acting on the particle is proportional to

Answer:

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