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...

  

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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) (D₂-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 (as² + 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. 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) (D₂-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 (as² + 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.

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