Free Energy in the Presence of an Applied Field

In the presence of an externally applied field (e.g., dc or low-fi equency electric, magnetic, or optical electric field), a corresponding interaction term should be added to the free energy. 

For an applied magnetic field H, the energy associated with it is 

The first term on the right-hand side of Equation (2.28) is independent of the orientation of the (anisotropic) molecules, and it can therefore be included in the 

On the other hand, the second term is dependent on the orientation of the molecules. Using Equation (2.10) for the order parameter 0ap we can write it as 

Therefore, the total free energy of a Hquid crystal in the isotropic phase, imder the action of an externally applied magnetic field, is given by 

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