Derive the Electric field expression for an insulating charg

Derive the Electric field expression for an insulating charged sphere of uniform spherical charge density radius R and total charge Q_total

Solution

Electrc field outside the sphere (r>R)

E.da=Q_tot/

E.4r²= Q_tot/

E= Q_tot/4r²

This is the electric filed outside the sphere

Electrc field inside the sphere (r<R)

The vloume charge density =Q_tot/V

=Q_tot/4r³/3

The charge contained with in the sphere of radius r

Q^’_tot=V =(4r³/3) Q_tot/4R³/3= Q_tot r³/R³

E.4r²= Q^’_{tot t}/

E= Q^’_tot /4r²

E= (Q_tot r³/R³)/ 4r²

E= (Q_tot/4R³) (r)