torque on a magnetic dipole or bar magnet in an uniform magnetic field

 Torque on a magnetic dipole or a bar magnet in an uniform magnetic field

 

1) Consider a bar magnet of length 2l is placed in a magnetic field of strength B.

 

2) Suppose the magnet is making 

angle with the magnetic field.

 

3) if m = strength of the pole of the magnet, then

a)           magnetic force acting on the north pole is

 

     F₁  =  mB (along the B direction, repulsive)

 

b)           magnetic force acting on the north pole is

 

     F₂  =  mB (opposite to the B direction, attractive)

 

Where  m = strength of the pole or magnetic moment of the bar magnet.

4) Now we see that these two forces F₁  &  F₂  are equal and opposite but they acting at different position of the same object. So, these forces will develop a torque on the Bar magnet.

5) Now the perpendicular distance between these two forces is

6) Now the torque acting on the magnet is

t   =    (Force)   ×    (perpendicular distance between them)

Since

M  =  m2l