A solid sphere of radius r has a charge Q distributed in its volume with a charge density `rho = kr^a` where k and a are constants and r is the distance from its centre. If the electric field at ` r = R//2` is `1//8` times that at `r = R` , find the value of a.

Answer

2

Explanation

From Gauss theorem, `E prop (q)/(r^(2))` ( q= charge enclosed)
`therefore (E_(2))/(E_(1)) = (q_(2))/(q_(1)) = (x_(1)^(2))/(x_(2)^(2)) = or B = ((int_(0)^(B) ( 4pi r^(2)) k r^(2) dr)/(int_(0)^(R//2) ( 4pi r^(2)) kr^(2) dr)) xx ((R//2)^(2))/((R)^(2))`, solving this equation we get a = 2