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# Electric Dipole in Electric Field

A system of two equal and opposite charges separated by a small fixed distance is called a dipole.

Dipole moment It is a vector quantity and is directed from negative charge to positive charge along the axis. It is denoted as and is defined as the product of the magnitude of either of the charge and the dipole length, i.e., (Fig. 15).

Fig. 15

Its S.I. unit is coulomb-metre or Debye (1 Debye = 3.3 × 10–30 C × m) and its dimensions are M0L1T1A1.

# Electric field and potential due to an electric dipole

Suppose a, e and g are three points on axial, equatorial and general position, respectively, at a distance r from the center of dipole.

Fig. 16

At axial point: Electric field and potential are given as

(directed from –q to +q)

Angle between is 0°.

At equatorial point: (directed from +q to –q) and Ve = 0. Angle between is 180°.

# Dipole in an external electric field

When a dipole is kept in an uniform electric field, the net force experienced by the dipole is zero, as shown in Fig. 17.

Fig. 17

The net torque experienced by the dipole is

⇒

Hence, due to torque so produced, the dipole aligns itself in the direction of electric field. This is the position of stable equilibrium of dipole.

Equilibrium of dipole: When θ = 0°, i.e., dipole is placed along the electric field, it is said to be in stable equilibrium, because after turning it through a small angle, dipole tries to align itself again in the direction of electric field.

When θ = 180°, i.e., dipole is placed opposite to electric field, it is said to be in unstable equilibrium.

Some Important Notes
• For a short dipole, electric field intensity at a point on the axial line is double than that at a point on the equatorial line on electric dipole, i.e., Eaxial = 2Eequatorial.
• It is interesting to note that dipole field (E  1/r3) decreases much rapidly as compared to the field of a point charge (E  1/r2).