A hollow dielectric sphere, as shown in figure, has inner and outer radii of `R_1 and R_2`, respectively. The total charge carried by the sphere is +Q, this charge is uniformly distributed `R_1 and R_2`.

a. the electric field for `rltR_1` is zero. `(Yes//No)`
b. the electric field for `R_1ltrltR_2` is given by ........... .
c. the electric field for `rgtR_2` is given by .......... .

Explanation

a. Yes, as there is no charge for `rltR_1`.
b. Volume charge density `rho = Q/(4/3pi(R_(2)^(3) - R_(1)^(3)))`
Charge with in radius r is q `= rho 4/3 pi (r^3-R_(1)^(3))`
`=(Q(r^3-R_(1)^(3)))/(R_(2)^(3)-R_(1)^(3))`

`E = (kq)/r^2 = Q/(4piepsilon_0r^2)[(r^3-R_(1)^(3))/(R_(2)^(3) - R_(1)^(3))]`
c For `rgtR_2`,
`E = 1/(4piepsilon_0) Q/r^2`