Find the potential energy of a system of four identical particles placed at the vertices of a
square of side l. Also obtain the potential at the centre of the square.
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The system can be made by bringing each charge from reference (∞) and
placing them on the vertices of the square
Then net work done in arranging the system = Potentital energy of teh system
For bringing 1st charge : W
1
=0
For bringing 2nd charge : W
2
l
2
kqq
(assuming each charge = q and side = l)
For bringing 3rd charge : W
3
=
l
2
kqq
+
(
2
l)
2
kqq
For bringing 4th charge: W
4
=
l
2
kqq
+
l
2
kqq
+
(
2
l)
2
kqq
Hence total work done = W
1
+W
2
+W
3
+W
4
=
l
2
5kq
2
i.e. potential energy of system
The potential at centra = 4×
(
2
1
)
2
kq
=
l
2
8kq
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