Electric Dipole - Special Condition of Torque
Description:
Let a dipole be placed in a uniform electric field, experiences a torque(τ). This torque is a variable whose value depends on θ ( torque (τ) = PEsin θ). This may very even if electric field (E) and dipole moment (P) do not change. Figure is shown below −
Special conditions for torque to vary in an electric field −
Let the dipole is placed along the direction of electric field. In this case (θ)=0
(τ) = PEsin(0) = 0
Rotate the dipole by 90 degree. In such case dipole is perpendicular to the electric field.
(τ) = PEsin(90) = PE
Rotate it again anticlockwise, so that P is in direction opposite to E(θ = 180)
(τ) = PEsin(180) = 0
Rotate the dipole again, such that the dipole is making 270 degree with the electricfield.
(τ) = PEsin(270) = -PE
On rotating the dipole more by 90 degree, dipole comes again to the same direction to that of electric field, so that (θ) = 0 or 360
(τ) = PEsin(360) = 0
Condition of equilibrium and non- equilibrium dipole
When the dipole experiences zero torque at θ = 0, 180, 360 and is not able to move in an electric field, it is called the equilibrium position of dipole.
In case, a dipole experiences some torque at θ = 90, 270, then the dipole is said to be in non-equilibrium or in unstable state.
When θ = 0o, 360o Or 180o. In all the cases torque experienced by dipole is zero and the dipole is said to be in equilibrium condition. But ;
At θ = 0o or 360o, a dipole is in stable state, because in such case, the dipole comes back to its original position even if the equilibrium is disturbed.
But when θ = 180o, the dipole remains in an unstable state, because in such case, the dipole does not come back to its original position when equilibrium is disturbed.