| |
which has the same dimension as that of
 The equation satisfied by is thus, |
| |
which is the differential form of Gauss's law for a dielectric medium.
Integrating over the dielectric volume, |
| |
where
 is the free charge enclosed in the volume. The volume integral can be converted to a surface integral using the divergence theorem, which gives |
| |
Thus the flux over the vector over a closed surface is equal to the free charged enclosed by the surface. |
| |
The above formulatons of Gauss's law for dielectric medium is useful because they refer to only free charges for which we may have prior knowledge. |
