Question

3. A point charge Q = 4 x 10-9 C is located at the origin. A spherical shell of dielectric material with &r = 3 is located between radii r=a and r=b, where a = 1 mm and b = 2 mm, while a second shell with material having Er = 5 is located between radii r=b and r=c, where c = 4 mm. Find numerical values for the magnitudes of the E-field, the D-field, and the polarization P at the radii r = 0.5 mm, r= 1.5 mm, and r = 3 mm.

Answer 1

yw 1 & 2 Ey=3 b/W 2 € Y , Eyes Q = 4*10-9 at 8=1.5 am (a) electric field at Y=3** < = x - y es en - 4x 109 x 9 x 100 = 36 X100 /m 5x (3xjogja I Pists a 2.4 P00 lm - 8 6 5/65 - torx y2 = 4X1079xgalog - 5.33 Xorum! 34 PS4/SX100 at r=asmm {= 4 1 10 9 x 9 410 Neno •So's & 10-6 (6) D Da Es Eo E so at 8=3mm D = 8X5E0 dios = 480 d 106 109/ at is om 0= 5.3383 %ok 100 = 16 Eo & loo teen 9 49 PIC m at o smm D = 144 Ep a 100 m (C) Polesization Pa to Me E = EolExt) & ( ze = {gos) so at g=3mm P = 89103 x Eo (5-1) = 328810S o/m at 8=1s p = {oke E t Eo (3-DX 5.33a 100 o/m = 10:687 Eo 1100 011m

now at 8=ois mm we know at 8=ous man there is only ais no electric medaim is there - so Eq=1 then te=0 thah P= (1-1) x = 0 at p=o7 at oz oo smm at 8= a. S m
if you have any doubts then comments below

Please give a thumb's up