Define the dipole moment of a magnetic dipole. Write its SI unit.Obtain the expression for the torque acting on a magnetic dipole placed in an external uniform magnetic field.

Magnetic dipole moment -  Magnetic dipole means magnetic south pole and north pole separated by a small distance. The magnetic dipole moment is the product of poles of magnet and distance between them or it is the product of the current flowing through coil and area.

It's SI unit is Am2.

Torque

consider the rectangular loop ABCD  with current I ampere flowing and having the number of turns N. The force acting on arm AD and BC is zero and the force is acted only on the arm AB and CD.

The arm AB exert a force $F_{1}$ and arm CD exert a force $F_{2}$

$F_{1}= IbB$

$F_{2}= IbB$

$\left | F_{1} \right |=\left | F_{2} \right |$ and the directions are opposite.

Therefore, the net force is zero. But it will experience a net torque.

We know that Torque = Force X Perpendicular distance between them

Therefore, $\tau = F_{1}\frac{a}{2}+ F_{2}\frac{a}{2}= IbB\frac{a}{2}+ IbB \frac{a}{2} = I(ab)B$

$\tau = IAB$

where A = ab is the area of the rectangle.

the number turns are N then,

$\tau =N IAB$

If the plane loop makes an angle with the magnetic field then the magnitude of torque become,

$\tau=NIABsin\theta$

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