Answer to Question #167447 in Quantum Mechanics for Reeshabh Kumar

Question

A Static electric field is distributed in a spherical shell of inner radius R1 and Outer radius R2 electric charge density is given by p= a+br ,where R is the distance from the centre and zero everywhere else.

(1). Find an expression for the electric field everywhere in terms of R.

Answer 1

1)

$$E=0, r<r_1$$

2)

$$Er^2=kQ=k\int_{r_1}^r(a+b)dr\\=k(a(r-r_1)+0.5b(r^2-r_1^2)\\ E=\frac{k}{r^2}(a(r-r_1)+0.5b(r^2-r_1^2), r_1<r<r_2$$

3)

$$E=\frac{k}{r^2}(a(r_2-r_1)+0.5b(r_2^2-r_1^2), r>r_2$$