SATHEE: electric-charges-and-fields Question 12

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Question: Q. 2. Two charges $q$ and $- 3 q$ are placed on $x$ -axis separated by distance $d$ . Where a third charge $2 q$ should be placed such that it will not experience any force? A [SQP 2017] [NCERT Exemplar]

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Solution:

Ans. At $P$ on $2 q$ , force due to $q$ is to the left and that due to $- 3 q$ is to the right.

$\begin{aligned} ∴ \frac{2 q^{2}}{4 π ε_{0} x^{2}} = \frac{6 q^{2}}{4 π ε_{0} (d + x)^{2}} & ∴ (d + x)^{2} = 3 x^{2} & ∴ 2 x^{2} - 2 d x - d^{2} = 0 & ∴ x = \frac{d}{2} \pm \frac{\sqrt{3} d}{2} \end{aligned}$

As the negative charge will be in between $q$ and $- 3 q$ , hence it is unacceptable.

$x = \frac{d}{2} \pm \frac{\sqrt{3} d}{2} \Rightarrow \frac{d}{2} (1 + \sqrt{3})$ to the left of $q$ .

[CBSE Marking Scheme, 2017] 2

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