Question

A dipole is released from rest a distance of 4m from a very long wire with a uniform linear charge density of 5nC/m. Describe the resulting motion of the dipole of its dipole moment vector is oriented (1) perpendicular to the wire, and (2) parallel to the wire

Answer 1

Let be the line charge density.

Electric field due to the uniform wire at a distance R

So we can assume electric field to be a constant in this region.

When we have a uniform electric field and dipole makes an angle with the field.

The net force on the dipole will be zero, since the positive and negative charge feels equal and opposite force. no translational motion will happen.

Even though forces are equal and opposite there are acting on two different points. Hence, it produces a torque , which will be product of dipole moment electric field and sine of angle between the previous vectors.

The dipole tend to align parallel to the field.

When the dipole moment is perpendicular to the wire, it makes 0 degree angle with the electric field.

. No rotation of the dipole.

When the dipole moment is parallel to the wire, it makes angle 90 degrees with electric field.

. Maximum torque and the dipole will rotate 90^o in this case.

Summary, No translational motion for the dipole since net orce is zero.

When it is parallel to electric field torque is also zero (no motion)

When it is perpendicular to electric field torque is maximum, dipole will roatate 90^o in order to align parallel to the applied field.