Question

Please help. I need all steps, please do not use the delta dirac function as some other answers have for this question

4. (30 pts) A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a frozen-in polarization , where A is a constant, and r (x, y, z), r x2 +y2 + z2 is the vector and the distance from the center, respectively. (a) (10 pts) Calculate bound surface and volume charge densities induced by polarization. (b) (10 pts) Calculate the field everywhere using Gauss's law (Eq. 2.13). (b) (10 pts) Calculate the displacement everywhere using Eq. 4.23 and then get the electric field from Eq. 4.21.

Answer 1

A thick spherical shell inner radius = a outer radius = b a is constant z = position vector r = squareroot x^2+y^2+z^2 bound charge density surface sigma b = p n or p r = a/e^2 sigma b = a/e^2 sigma a = -a/a^2 sigma b = +a/b^2 volume charge densities sb = -nabla^bar p6bar r^bar sb = -1/r62 d.dr a/r^2 sb = -4a/r^3 in region r < a no charge inside the shell q enclosed = 0 e 4pir^2 e^cap = enclosed/eo = 0 e = 0 q_bound = sigma_b 4 pi r^2 = -a/c62 4 pi r^2 q = -4pi km e = -potassiume^2 eo e^cap and in region > b: e^bar = 0