Two concentric uniformly charge spherical shells of radius `R_(1)` and `R_(2) (R_(2) gt R_(1))` have total charges `Q_(1)` and `Q_(2)` respectively. Derive an expression of electric field as a function of r for following positions.
(i) `r lt R_(1)` (ii) `R_(1) le r lt R_(2)`
(iii) `r ge R_(2)`

Explanation

(i) for `r lt R_(1)`,
therefore point lies inside both the spheres
`E_("net")=E_("inner")+E_("outer")=0`
(ii) for `R_(1) le r lt R_(2)`,
therefore point lies outside inner sphere but inside outer sphere :
`E_("net")=E_("inner")+E_("outer")=("KQ"_(1))/(r^(2))hatr+0`
`=("KQ"_(1))/(r^(2))hat r`
(iii) for `r ge R_(2)`
point lies outside inner as well as outer sphere therefore.
`E_("Net")=E_("inner")+E_("outer")`
`=(KQ_(1))/(r^(2))hat r+(KQ_(2))/(r^(2))hat r`
`=(K(Q_(1)+Q_(2)))/(r^(2))hat r`