A parallel plate capacitor with a nonuniform dielectric
The dielectric of a parallel plate capacitor has a permittivity that varies as ero+ax, where x is the distance from one plate. The area of a plate is A, and their spacing is s.
(a) Find the capacitance.
(b) Show that, if er varies from ero to 2ero, then c is 1.44 times as large as if a were zero.
(c) Find P from the values of D and E for that case.
(d) Deduce the value of rb.
(e) Now calculate rb from the relation given in problem 7-2 [Prob 7-2: show that in a non homogeneous dielectric, if rf = 0, then
rb = (ero/er) E.grad er]
(f) Draw curves of e, rb and P as functions of x for ero = 3.00, a = ero/s, s = 1.00 mm when the applied voltage is 1.00 volts.