when dipole is placed in a uniform electric field net force on it is 0 but torque is not 0. but according to formula τ=rFsinθ, as F is 0 so τ should be 0?

CBSE Class 12-science Answered

when dipole is placed in a uniform electric field net force on it is 0 but torque is not 0. but according to formula τ=rFsinθ, as F is 0 so τ should be 0?

Asked by rohitraman1115 | 27 Nov, 2019, 07:17: PM

Expert Answer

Consider a permanent dipole of dipole moment p in a uniform external field E, as shown in Figure.

(By permanent dipole, we mean that p exists irrespective of E; it has not been induced by E.)

There is a force qE on q and a force –qE on –q. The net force on the dipole is zero, since E is uniform.

However, the charges are separated, so the forces act at different points, resulting in a torque
on the dipole. When the net force is zero, the torque (couple) is independent of the origin.

Its magnitude equals the magnitude of each force multiplied by the arm of the couple (perpendicular
distance between the two antiparallel forces).

Magnitude of torque, |τ| = q E × 2 a sinθ = 2 q a E sinθ ................(1)

Its direction is normal to the plane of the paper, coming out of it.

We know that dipole moment is defened as, p = q × 2a...............(2)

Using eqn.(2) and from the definition of vector product ( cross product), we write eqn.(1) as ,

τ = p x E

Direction of torque τ is normal to the paper, coming out of it.

This torque will tend to align the dipole with the field E. When p is aligned with E, the torque is zero.

Answered by Thiyagarajan K | 27 Nov, 2019, 10:03: PM