Consider a spherical plastic shell with inner radius r=1cm, r2=2cm, and a dielectric constant K=4. The center is hollow. Free charge is bound within the plastic. The charge distribution is spherically symmetric but decays with radius, following a charge density:p_f=K/r where K=20uC/m^2 is constant.

Question

Consider a spherical plastic shell with inner radius r=1cm, r2=2cm, and a dielectric constant K=4. The center is hollow. Free charge is bound within the plastic. The charge distribution is spherically symmetric but decays with radius, following a charge density:p_f=K/r where K=20uC/m^2 is constant.
a) what is the total amount of free charge embedded in the plastic in coulombs?
b)What bound surface charge is induced on the outer surface of the plastic, in C/m^2?