Question

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)`

Answer 1

(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)`, 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)`