A spherical nonconducting shell of inner radius r120cm and o

A spherical, non-conducting shell of inner radius r_1=20cm and outer radius r_2=25cm carries a total charge Q=25microC distributed uniformly throughout the volume of the shell. It is surronded by an electrically neutral concentric conducting shell of inner radius 40cm and outer radius 45cm. Draw the appropriate Gaussian surface and calculate the electric field: (a). at a distance r=15cm from the center of the shells. (b). at a distance r=22cm from the center of the shells. (c.) a distance r=30cm from the center of the shells. (d.) at a distance r=42cm from the center of the shells. (e.) at a distance r=50cm from the center of the shells. PART B: what is the charge, if any, on the inner surface of the conducting shell? What is the charge, if any, on the outer surface of the conducting shell?

Solution

Volume of non-conducting shell V =(4/3)pi (25³ - 20³ ) =31940 cc

a) guassian surface r= 15 cm

charge enclosed q=0 electric fied e= 0

b) r = 22 cm volume of the charge contained = (4/3)pi (22³ - 20³ ) = 11092 cc

charge enclosed q = 25e-6 * 11092/31940 = 8.68e-6 C

E = kq/r² 8.9e+9 8.68e-6 / (0.22)²   = 1596e+3 N/C

c) r= 30 cm

charge enclosed q = 25e-6 C

E =8.9e+9*25e-6/(0.3)² =2472e+3 N/C

d) r= 42 cm, the point is inside the condcuting shell and field inside a conductor =0

charge induced on the inner surface of the shell = -25e-6 C

e) r =50 cm

net charge enclosed = 25e+6 C

E = 8.9e+9*25e-6 /(0.5)² =890e+3 N/C

charge induced on the inner surface of the conducting shell = -25e-6 C

charge induced on the outer surface of the conducting shell = 25e-6 C