$word_{count}$: 280

An electric dipole consists of two equal and opposite charges +q and -q separated by distance 2a. The dipole moment p = q(2a) is a vector pointing from -q to +q, with SI unit C m. Dipoles are fundamental in molecular physics (polar molecules like water) and dielectric theory.

Far-field approximation (r >> a): Axial field: $E_{axial}$ = 2kp/$r^3$ (along p direction). Equatorial field: $E_{eq}$ = $\frac{kp}{r}$^3 (opposite to p direction). The axial field is always twice the equatorial field at the same distance. General point at angle theta from axis: E = (kp/$r^3$)*sqrt(1 + 3$cos^2$(theta)). All dipole fields fall as 1/$r^3$.

In a uniform external field E: The dipole experiences zero net force (forces on +q and -q cancel) but a torque tau = p x E with magnitude pEsin(theta). The torque aligns p with E. Potential energy U = -p.E = -pEcos(theta). Stable equilibrium at theta = 0 (U = -pE, minimum). Unstable equilibrium at theta = pi (U = +pE, maximum). Work to rotate from $theta_1$ to $theta_2$: W = pE(cos($theta_1$) - cos($theta_2$)). Work for full rotation (0 to pi): W = 2pE.

In a non-uniform field: The dipole also experiences a net translational force F = (p.nabla)E, directed toward stronger field region when aligned. This explains why neutral objects are attracted to charged objects — the induced dipole moment aligns with and moves toward the stronger field.

JEE frequently tests: axial vs equatorial field comparison, torque calculation, work done in rotation, and the distinction between uniform (torque only) and non-uniform (torque + force) field situations.