5. Basic Equations in Dielectrics VxE-0, E-P 60 Pi+ Pp (CoE+P) = -D=pt, D=coE+P P=cox.E, D=co(1 + Xe)E = E When D and E are known, we have P=(-co)E-co where/co is the dielectric constant. 6. Boundary Conditions I (1) = 6 (-1) E > 7. Boundary Conditions II Dan-Din=0 Ex Ex (7) (8) (9) (10) (D-P) (D-P).i -> Ez Et (11) - dn dez dus dn dees-01. (12) 2-dres (13) 8. Consider a point charge q in a dielectric medium with Keg. Derive the following expressions for the electric displacement, field and polarization are 9 g(-1) 4K 9. Homework Due on 23.08.2022: Consider a uniformly polarized sphere of radius R such that Pak. Use op and p, and for a point r along the axis, to show that, 2p P outside Eoutside t k, p=R P 402 Po Vinside Enaide Pok 360 (14) (15) 360 Resolve this problem by making use of the expansion of in terms of Legendre polynomials. 10. Homework Due on 23.08.2022: A thin dielectric rod of cross section A extends along the -axis from: -L to L. The polarization of the rod is along its length such that (a) find the polarization volume charge density and the corresponding charge q (as + b) k. (b) find the polarization surface charge density at each end and the corresponding charge q 11. Homework Due on 23.08.2022: A dielectric cylinder of radius R extends from :=-L to := L. Let the polarization of the cylinder be of the form Par, where a is a constant, (a) find the polarization volume charge density and the corresponding charge qp, (b) find the polarization surface charge density at each surface and the corresponding charge q.