By Gauss’s law
E × 4 p r 2 = 
2
0
4
R
εσ
π
Or,  
2
2
2
0
0
4
R
q
E
r
r
εσ
ε
=
=
π
where q  =  4 p R2 s is the total charge on the spherical shell Vectorially,
2
0
ˆ
4
q
εr
=
π
E
r
(1 34)
The electric field is directed outward if q > 0 and inward if
q < 0 This, however, is exactly the field produced by a charge
q placed at the centre O