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 at 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`.

Explanation

Let the arbitrary radius x.
The charge on sphere.
`= (4/3 pi (x^3 - (r_(1)^3))q/ 4/3 pi ((r_(2)^3)-(r_(1)^2)))`
`= ((x^3 - (r_(1)^3)/ (r_(2)^3 - r_(1)^3)) q `
According to Gauss's law
` int E ds = q / epsilon_0`
` E. 4 pi x^2 = ((x^3-(r_(1)^3))/((r_(2)^3)-(r_(1)^3))) (q/epsilon_0)`
` or E = (q (x^3 - r_1^3)/ 4 pi epsilon_0 (x^2) (r_(2)^3 - r_(1)^3)` .