An isolated metal of radius r is given a charge q . The potential energy of the spere is
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Answer:
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Explanation:
Let at any instant q be the charge on the sphere
Now potential of the sphere =
r
kq
Work done to add a dq charge to this sphere
dw=
r
kq
⋅dq (As V
∞
=0)
∴ total work done to accumulate q charge is
∫dw=∫
0
q
r
kq
⋅dq
⇒w=
r
k
[
2
q
2
]
0
q
⇒w=
2r
kq
2
⇒w=
4πε
0
r⋅2
q
2
⇒w=
8πε
0
r
q
2
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