The total free energy of a dielectric LL8 Section 11

Dielectric (need not extend to infinity) Electric field includes contributions from both extraneous charge on the conductor and polarization charge in the dlelectric

F is free energy with respect to charge on conductors. For given charges and constant T, F is a minimum. Irreversible changes occur until F is minimized and equilibrium is established.

Field that would be present if dielectric were gone. Old definition of free energy: New definition: Difference has nothing to do with dielectric, so the new definition gives the same thermodynamics.

If the field is changed infinitesimally while maintaining equilibrium at constant T…

The change in due to a change in the field, caused by a reversible change in the charges

Dielectric in a uniform external field. conductors Total electric dipole moment If we allow temperature to change, then

Total dipole moment = negative change in free energy at constant temperature divided by the change in the external field

For a linear isotropic dielectric, D =  E Using new definition of free energy of dielectric F Subtract cross terms

Charge on conductor First integralNo extraneous charge in the dielectric No charge in vacuum Potentials are constant on surface of conductor Since

Second integral Total dipole moment of dielectric For uniform external field

For arbitrary dielectric For linear dielectric P must be a linear function of : + const Same result

For linear dielectric, we can more generally write As for conductors For conductors  depends only on shape For dielectric  also depends on  Order of derivatives doesn’t matter:

For a weak or dilute dielectric  ~ 1, e.g. a gas. Susceptibilityis small. Then the fieldis not changed much by the dielectric Assumed uniform