12th physics electric charges and fields- Electric Dipole & Dipole in a Uniform External Field

Electric Dipole & Dipole in a Uniform External Field

Electric Dipole − System of two equal and opposite charges separated by a certain small distance.

Electric Dipole Moment − It is a vector quantity, with magnitude equal to the product of either of the charges and the length of the electric dipole

Its direction is from the negative charge to the positive charge.

Electric Field on Axial Line of an Electric Dipole

Let P be at distance r from the centre of the dipole on the side of charge q. Then,

Where, is the unit vector along the dipole axis (from − q to q). Also,

The total field at P is

For r >> a

Electric Field for Points on the Equatorial Plane

The magnitudes of the electric field due to the two charges +q and −q are given by,

The directions of E_+q and E_−q are as shown in the figure. The components normal to the dipole axis cancel away. The components along the dipole axis add up.

∴ Total electric field

[Negative sign shows that field is opposite to]

At large distances (r >> a), this reduces to

Dipole in a Uniform External Field

Consider an electric dipole consisting of charges −q and +q and of length 2a placed in a uniform electric field making an angle θ with electric field.

Force on charge −q at (opposite to)

Force on charge +q at (along)

Electric dipole is under the action of two equal and unlike parallel forces, which give rise to a torque on the dipole.

τ = Force × Perpendicular distance between the two forces

τ = qE (AN) = qE (2a sin θ)

τ = q(2a) E sinθ

τ = pE sinθ