Question

21 A nonconducting spherical shell, with an inner radius of 40 nd an outer radius of 6.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The vo ume charge density ρ is the charge per unit volume, with the unit coulomb per cubic meter. For this shell p bir,where r is the distance in meters from the center of the shell and b-3.0 uC/m2. What is the net charge in the shell?

Answer 1

21. given a non conducting spherical shell
   inner radius, ri = 4 cm
   outer radius, ro = 6 cm
   volume charge density = rho = b/r
   b = 3 uC/m^2

   net charge in the shell = q
   for thin shell of thickness dr at radius r

   dq = rho*4*pi*r^2*dr = 4*pi*b*r*dr
   hence
   q = integral(dq) from ri to ro
   q = 2*pi*b(ro^2 - ri^2) = 2*pi*3uC(0.06^2 - 0.04^2) = 0.0376991118430 uC