Electric DipoleJEE Main

Axial vs equatorial fields — the 1/r³ world — interactive Physics simulation for IIT-JEE.

Concept

Equal and opposite charges a small distance apart form a dipole — the fundamental neutral-but-polar object. Its monopole fields cancel, leaving a field that dies as 1/r³ (faster than a point charge's 1/r²). On the axis the field is twice the equatorial value and points along $\vec p$ ; on the equator it points opposite to $\vec p$ .

Key formula

E_{axial} = \frac{2kp}{r^3}, \qquad E_{eq} = \frac{kp}{r^3}, \qquad \vec\tau = \vec p \times \vec E, \qquad U = -\vec p\cdot\vec E

Derivation

Superpose the two point-charge fields. On the axis they nearly cancel but the nearer charge wins; expanding $(r\mp a)^{-2}$ for $r \gg a$ leaves the $2kp/r^3$ term.

On the equator the transverse components cancel and the parallel components add to $kp/r^3$ , anti-parallel to $\vec p$ . In an external field the net force is zero (uniform E) but the torque $pE\sin\theta$ aligns the dipole.

Scenarios to explore

Electric Dipole — Axial vs equatorial fields — the 1/r³ signature.

Real-world applications

Water's permanent dipole — microwave ovens torque it billions of times a second.
Antenna radiation patterns are dipole fields.
Dielectric polarization = aligning molecular dipoles.

JEE exam tips

Axial = 2 × equatorial at the same distance — the signature ratio.
Potential: V = kp cosθ/r² — zero everywhere on the equatorial plane.
Stable equilibrium at θ = 0 (U = −pE), unstable at θ = 180° (U = +pE).

Common mistakes

Using 1/r² fall-off — dipole fields go as 1/r³.
Forgetting E_axial is parallel to p while E_equatorial is ANTI-parallel.
Torque zero at θ = 90° — no, torque is MAXIMUM there; it's zero at 0° and 180°.

Exam traps to avoid

In a NON-uniform field a dipole feels a net force (toward stronger field if aligned).
Work to rotate from 0° to 180° is 2pE; from 0° to 90° is pE.