This is because
the field at any point on the spherical Gaussian surface has the
same direction as the normal to the surface there,  and has the same
magnitude at all points on the surface The charge q enclosed by the Gaussian surface is the positive nuclear
charge and the negative charge within the sphere of radius r,
i e , 
3
4
3
r
q
Z e
ρ
π
=
+
Substituting for the charge density r  obtained earlier, we have
3
3
r
q
Z e
Z e
R
=
−
Gauss’s law then gives,
2
3
0
1
( )
;
4
Z e
r
E r
r
R
r
R
ε
 
 
=
−
<
 
 
 
 
π
The electric field is directed radially outward