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 This is given by (charge at D) × (potential at D due to charges at A,
B and C)
      = −
+
+
−
+




q
q
d
q
d
q
d
4
4
2
4
0
0
0
π
π
π
ε
ε
ε
=
−
−


q
d
2
0
4
2
1
2
πε
Rationalised 2023-24
Physics
58
 EXAMPLE 2 4
Add the work done in steps (i), (ii), (iii) and (iv) The total work
required is
=
−
+
+
−

 +
−






q
d
2
0
4
0
1
1
1
2
2
1
2
πε
( )
( )
 =
−
(−
)
q
d
2
0
4
4
2
πε
The work done depends only on the arrangement of the charges, and
not how they are assembled