Torque on a Current Carrying Coil in a Magnetic Field
When an electric current flows in a closed loop of wire, placed in a uniform magnetic field, the magnetic forces produce a torque which tends to rotate the loop so that area of the loop is perpendicular to the direction of the magnetic field.
Consider a rectangular coil PQRS placed in an external magnetic field as shown in diagram (a). Let 'I' be the current flowing through the coil. Each part of the coil experiences one Lorentz. Each part of the
forces is as shown. The forces
are equal in magnitude but act in opposite directions along the same straight line. Hence they cancel out.
These two forces constitute a couple and so rotates the coil in the anticlockwise. The torque
If the coil has N turns then
where pm = NIA is called the magnetic dipole moment of the loop.
Note:
Magnetic Dipole Moment of a Revolving Electron
The Bohr's atom model pictures the electrons to revolve around stationary heavy nucleus of change +ze.
The moving electron constitutes a current where e is the electronic charge and T the time period of revolution.
Also where v is its orbital velocity and the radius
of the orbit. The small magnetic moment ml associated with this revolving current is
Multiplying and dividing R.H.S by me we have
Where l = m v r, the angular momentum. The negative sign indicates
is opposite to
.
The above expression helps to explain magnetic properties of
materials. Besides the orbital magnetic moment
,
electrons also possess spin magnetic moment. The origin of magnetism in iron and other materials can be traced to this magnetic moment.
as shown. The forces
are equal in magnitude but act in opposite directions along the same straight line. Hence they cancel out.
where e is the electronic charge and T the time period of revolution.
where v is its orbital velocity and the radius
of the orbit. The small magnetic moment ml associated with this revolving current is
is opposite to
.