A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

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Solution

Q.
A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

1 (4d/3, 0 , 0)

2 (d/4, 0 , 0)

3 (3d/4, 0 , 0)

4 (d/3, 0 , 0)

Ans.
(2)

Let $E_{P} = 0$

$∴ \frac{k q}{x^{2}} = \frac{k 9 q}{{(d - x)}^{2}} \Rightarrow \frac{d - x}{x} = 3 \Rightarrow x = \frac{d}{4}$

$∴$ co-ordinate of P is $(\frac{d}{4}, 0, 0)$

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