For a short dipole placed at origin O, the dipole moment P is along x -axis, as shown in the figure. If the electric potential and electric field at A are V₀ and E₀, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y -axis is given by (a) V₀/2 and E₀/16 (b) zero and E₀/8 (c) V₀ and E₀/4 (d) zero and E₀/16

Answer: (d). A is on the axis at r: V₀ = kp/r², E₀ = (2kp)/(r³). B is on the equatorial line, so VB = 0. EB = (kp)/((2r)³) = (kp)/(8r³) = E₀/16 So the answer is (d) zero and E₀/16.

For a short dipole placed at origin O, the dipole moment P is along x… | JEE Main 2025 (22 Jan, Shift 2)

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Electric Dipole

For a short dipole placed at origin O, the dipole moment P is along $x$ -axis, as shown in the figure. If the electric potential and electric field at $A$ are $V_0$ and $E_0$ , respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the $y$ -axis is given by

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Answer: (d)

A is on the axis at $r$ : $V_0 = \frac{kp}{r^2}$ , $E_0 = \frac{2kp}{r^3}$ .
B is on the equatorial line, so $V_B = 0$ .
$E_B = \frac{kp}{(2r)^3} = \frac{kp}{8r^3} = \frac{E_0}{16}$
So the answer is (d) zero and $\frac{E_0}{16}$ .

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