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 + 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))hat(r) + 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 )`