Problem 3 Two round conductors are concentrically nested as

Problem 3 Two round conductors are concentrically nested as shown in the cross-sectional inner sphere has a radius of a-3 cm and a net charge of +12 pct The outer spherical shell has an inner radius of b-6 cm, an outer radius of c-8 cm, and a net charge of-6 C. Note is 10-3 diagram below. T (a) Determine the net charge and the charge density on each surface (ie at r=a, r b, and r=c). (b) Find the electric field as a function of r from r-0 to r-10 cm. Plot the field magnitude as a function of r

Solution

a) at r= a

charge = 12 uC = 12 x 10^-9 C

charge surface density = Q / (4pia^2)

= (12 x 10^-9) / (4 x pi x 0.03^2) = 1.06 x 10^-6 C/m^2

at r= b

charge = -12 uC

charge surface density = (-12 x 10^-9) / (4 x pi x 0.06^2)

= - 2.65 x 10^-7 C/m^2

at r= c

charge = -6uC - (-12uC) = 6 uC

charge surface density = (6 x 10^-9) / (4 x pi x 0.08^2)

= 7.46 x 10^-8 C/m^2

b) for r < 3 cm

field inside conductor is zero.

E = 0

for 3 =< r < 6 cm

E ( 4 pi r^2 ) = (12 uC) / e0

E = 12uC / 4pie0r^2 Or k(12uC) / r^2 or 107.85/r^2

for 6 < r < 8

E = 0

for r > 8

E ( 4 pi r^2 ) = (12 uC -6uC) / e0

E = 6uC / 4pie0r^2 Or k(6uC) / r^2 or 53.93/r^2