Magnetism - Dipoles - Physics 299

Application of the expression for the force on a current carrying wire to the top and bottom sides of the rectangle leads to cancellation of forces as shown.

The forces on the other two sides (length a) are also equal and opposite, as shown in (b) above, . Although the net force in this case is zero, because the forces are not co-linear, there is a net torque on the current loop, given by

The magnitude of this torque is given by

where A = ab is the cross section area of the coil.

The magnitude of the magnetic dipole moment of the loop with N turns is defined by,

μ is a vector quantity whose direction is perpendicular to the loop with a sense defined by (another) Right Hand Rule.

With this definition of μ the torque on the current loop is given by

Without proof, the potential energy of a magnetic dipole in an external magnetic field is given by

Note that the above expressions for the torque and potential energy of a magnetic dipole in an external magnetic field are identical in form to those obtained for an electric dipole in an external electric field.

and

Magnetic Dipoles