A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in figure. The point P is alao on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q se

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Solution

Q.
A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation [2025]

1 $\frac{a}{r} ~ 20$

2 $\frac{a}{r} ~ 10$

3 $\frac{a}{r} ~ 0.5$

4 $\frac{a}{r} ~ 3$

Ans.
(4)

$\Rightarrow \frac{1}{{(r - a)}^{2}} - \frac{1}{{(r + a)}^{2}} = \frac{2 a}{{(a^{2} + r^{2})}^{3 / 2}}$

$\frac{4 a r}{{(r^{2} - a^{2})}^{2}} = \frac{2 a}{{(a^{2} + r^{2})}^{3 / 2}}$

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