Charge is distributed within a solid sphere of radius r_0 in such a way that the charge density is a function of the radial position within the sphere of the form: ρ_E(r)=ρ_0(r/r_0).

 

a) If the total charge within the sphere is Q (and positive), what is the magnitude of the electric field everywhere within the sphere in terms of Q, r_0, and the radial position r ?

Express your answer in terms of the variables Q, r_0, r, and appropriate constants.

 

b) What is the direction of the electric field everywhere within the sphere? 

   Choose between 

   i) radially inward

    OR

   ii) radially outward