A point particle of charge Q is located at P along the axis of an… | JEE Main 2025 (23 Jan, Shift 1)

Q28JEE Main 2025 · 23 JAN · SHIFT 1Medium

Electric Dipole

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?

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Answer: (b)

Dipole 1 (axial, exact): $E_1 = kq\left[\frac{1}{(r-a)^2} - \frac{1}{(r+a)^2}\right] = \frac{4kqar}{(r^2 - a^2)^2}$
Dipole 2 (equatorial, exact): $E_2 = \frac{2kqa}{(r^2 + a^2)^{3/2}}$ ; from the figure the two fields at P are opposite.
No force: $2r(r^2 + a^2)^{3/2} = (r^2 - a^2)^2$ , i.e. $2(1 + t^2)^{3/2} = (1 - t^2)^2$ with $t = \frac{a}{r}$ .
$t = 3$ : LHS $= 2\times10^{3/2} \approx 63.2$ , RHS $= 64$ , nearly equal.
So the answer is (b) $\frac{a}{r} \sim 3$ .

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Electric Dipole question from JEE Main 2025 (23 Jan, Shift 1)

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