A Charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii `r_1` and `r_2` (figure 30-E4). Find the electric field at a point P a distance x away from the centre for `r_1ltxltr_2`. Draw a rough graph showing the electric field as a function of x for `0ltx lt2r_2`. (figure).

Explanation

Draw a sphere of radius `x` with centre `O`. The charge contained in spherical shell of inner radius `r_(1)` and outer radius `x` is given by
`q = (Q)/((4)/(3) pi (r_(2)^(3) - r_(1)^(3))) (4)/(3) pi (x^(3) - r_(1)^(3))`
`= (Q(x^(3) - r_(1)^(3)))/((r_(2)^(3) - r_(1)^(3)))`
Assume this charge to be concentrated at centre `O` and apply formula of point charge.
`E = (1)/(4 pi in_(0)) (q)/(x^(2))`
`= (1)/(4 pi in_(0)) (Q(x^(3) - r_(1)^(3)))/(x^(2) (r_(2)^(3) - r_(1)^(3)))`