Langevins Theory Of Paramagnetism

Langevin's Theory of Paramagnetism: Langevin assumes that each atom has a permanent magnetic momentum m. The only force acting on atom is that due to the external field B Let θ be the angle of inclination of the axis of the atomic dipole with the direction of the applied field B Then magnetic potential energy of the atomic dipole is

Now, on classical statistics, the number of atoms making an angle between

Where  K  is Boltzmann’s constant and T is the absolute temperature

Hence the total number of atomic magnets in unit volume of paramagnetic material

The component of each dipole moment parallel to B in McosθThe total magnetic moment of all the n atoms contained in unit volume of the gas is the magnetization M. it is given by

Evaluating integral and substituting the value of C from (3), we get

The variation of M with α is shown in figure 1.