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

(1) Intial direction of Dipole = - X-axis Initial velocity of Dipole = 0 m/s

Direction of wire = Y-axis Charge per unit length on wire = 5 X 10^(-9) C/ m

Distance from wire = X = -4 m

Since Charge on wire is positive, at a distance r from the wire parallel to X-axis, E field is radially outward

Since Dipole is oriented perpendicular to wire,

The Torque = p E sin , where p is magnitude of Dipole Moment , E the magnitude of Electric field in which dipole is present and is angle between Dipole Moment vector and E Vector.

In this case Torque is zero , So only Coloumb force due to E field of the wire acts on the dipole . The +ve charge of dipole is repelled along -X-axis while -ve charge is attracted. Since -ve charge is slightly nearer to E field , there will be net attraction towards wire and the Dipole will accelerate along +X-direction

2) p is parallel to the wire

So Torque = p E sin 90 = pE

The net torque causes angular acceleration of the dipole in counter-clock-wide direction and hence the dipole develops an angular acceleration.