Question

a spherical shell of charge of uniform density . Plot E for distance r from the center of the shell ranging from zero to 30 cm. Assume that  = 1.010-6 C/m3, a = 10 cm and b = 20 cm.

Answer 1

If the shell is made of a non-conducting material, the field inside the shell (if a=10 cm is the radius of the cavity) is zero:

$$0<r<a: E_1=0.$$

The field outside the shell is easy to find and it's described with the same equation as for a point charge:

$$r>b: E_3=\frac{1}{4\pi\epsilon_0}\cdot Q/r^2,\\ \space\\ Q=\rho\cdot\frac{4}{3}\pi b^3,\\ \space\\ E_3=\frac{\rho b^3}{3\epsilon_0r^2}.$$

The field within the material inside b-a = 20-10 = 10 cm can be described with the equation shown below that can be derived from Gauss's law:

$$a<r<b: E_2=\frac{(r^3-a^3)\rho}{3r^2\epsilon_0}.$$

The field: