Question

A plate of thickness $$h$$ made of uniform statically polarized dielectric is placed inside a capacitor whose parallel plates are inter-connected by a conductor. The polarization of the dielectric is equal to $$P$$ (Fig.). The separation between the capacitor plates is $$d$$. Find the strength and induction vectors for the electric field both inside and outside the plates.

Answer 1

Since the condenser plates are connected,
$$E_{1}h + E_{2}(d - h) = 0$$
and $$P + \epsilon_{0} E_{1} = \epsilon_{0} E_{2}$$
or, $$E_{1} + \dfrac {P}{\epsilon_{0}} = E_{2}$$
Thus, $$E_{2} d - \dfrac {Ph}{\epsilon_{0}} = 0$$, or, $$E_{2} = \dfrac {Ph}{\epsilon_{0}d}$$
$$E_{1} = -\dfrac {P}{\epsilon_{0}} \left (1 - \dfrac {h}{d}\right )$$.