Torque Due To Dipole In A Uniform External Field

Consider a permanent dipole of dipole moment p in a uniform external field E, as shown in Fig. 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 anti-parallel forces). Magnitude of torque = q E × 2 a sinθ = 2 q a E sinθ.

Its direction is normal to the plane of the paper, coming out of it. The magnitude of p × E is also p E sinθ and its direction is normal to the paper, coming out of it. Thus,

t = p × E

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

In that case, the net force will evidently be non-zero. In addition there will, in general, be a torque on the system as before.

The general case is involved, so let us consider the simpler situations when p is parallel to E or anti-parallel to E. In either case, the net torque is zero, but there is a net force on the dipole if E is not uniform.

It is easily seen that when p is parallel to E, the dipole has a net force in the direction of increasing field. When p is anti-parallel to E, the net force on the dipole is in the direction of decreasing field.

In general, the force depends on the orientation of p with respect to E.

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: what are the characteristic of charges acquired by the objects on rubbing against each other?

Q2: Who suggested first that there are two kinds of charges?

Q3: How can you show that there are two types of charges?

Q4: An ebonite rod is rubbed with the fur or wool. What type of charges do they acquire?

Q5: Is mass of body affected on charging?

Q6: What is the polarity of charge?

Answer these questions in comment box and help your friends