A solid, non-conducting sphere of radius R possesses a volume charge density that varies with radial distance according to ρ(r)=ρ0Rr, where ρ0 is a positive constant.
a. (i) Obtain an expression for the total charge contained within the sphere.
b. (ii) Derive the expression for the magnitude of the electric field as a function of the distance r from the centre for (a) r<R and (b) r≥R.
c. (iii) Show that the electric field attains a maximum value at a certain distance rm inside the sphere and determine rm in terms of R.