Electric Field Intensity due to a Point Charge in a Material Medium

Consider a point charge q placed at a point O inside a medium of dielectric constant K (Fig. 10.7). At a point P, a distance r from O, a small positive test charge $q_0$ experiences a Coulomb force (using the medium form of Coulomb's law from section 10.4.2), $\vec{F}=\frac{1}{4\pi\epsilon_0K}\frac{qq_0}{r^2}\hat{r},$ where $\hat{r}$ is the unit vector directed along OP.

The precise, formal definition of electric field is the LIMIT of the force per unit test charge as the test charge is shrunk to be vanishingly small, $\vec{E}=\lim_{q_0\to0}\frac{\vec{F}}{q_0}.$ Taking this limit matters conceptually: the test charge must be a small POSITIVE charge, small enough in magnitude that it does not itself disturb or alter the field of the source charge being measured -- if the test charge were too large, it would perturb the very field it is being used to probe. …