The total work needed can
be calculated in steps:
(i)
Work needed to bring charge +q to A when no charge is present
elsewhere: this is zero (ii) Work needed to bring –q to B when +q is at A This is given by
(charge at B) × (electrostatic potential at B due to charge +q at A)
= −
× 


 = −
q
q
d
q
d
4
4
0
2
0
π
π
ε
ε
(iii) Work needed to bring charge +q to C when +q is at A and –q is at
B This is given by (charge at C) × (potential at C due to charges
at A and B)
= +
+
+
−




q
q
d
q
d
4
2
4
0
0
π
π
ε
ε
      =
−
−

q
d
2
0
4
1
1
2
πε
(iv) Work needed to bring –q to D when +q at A,–q at B, and +q at C