The magnetic field at the centre of a coil of radius R and number of turns N , carrying a current I is . At a point distance x from the coil, the field is

At a point distance r from the coil, the magnetic field is . If is neglected in the denominator;

If the length of the wire is L and the radii of the coils in two cases be and . Then,

Magnetic moment of the electron .The current due to the orbiting electron

. The magnetic moment

the work done to turn a needle through an angle θ is The torque needed to maintain ..

The magnetic moment associated with a coil carrying current is given by the product of its area and the current through it. M=n I A

The potential energy of a magnetic dipole of moment m placed in a magnetic field is When the magnet is aligned in the direction of the field, and the initial potential energy When the magnet is aligned opposite to the direction of the fieldits potential energy isWork done in rotating the magnet is equal to the change in its potential energy.

The potential energy of a magnetic dipole of moment m placed in a magnetic field is .When the magnet is aligned in the direction of the field, and the initial potential energy When the magnet is placed perpendicular to the direction of the field,its potential energy is .Work done in rotating the magnet is equal to the change in its potential energy.

A solenoid carrying current produces a magnetic field very similar to that of bar magnet. The magnetic field lines emerge from the ends of a solenoid and the number of field lines near its perpendicular bisector is almost equal to zero. A circular coil produces field along its axis. A straight conductor produces a magnetic field that can be represented by concentric circles. A toroid is a solenoid that has collapsed on itself. The field in a toroid is confined to the ring like region bounded by the toroid.