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The potential energy of the system of tw...

The potential energy of the system of two identically charged spheres as shown in the figures is equal to (Assume the charge distribution to be uniform)

A

`(q^(2))/(4piepsilon_(0))[(1)/(R)+(1)/(r)]`

B

`(1)/(4piepsilon_(0))(q^(2))/(r)`

C

`(1)/(4piepsilon_(0))(q^(2))/(q(R+r))`

D

None of these

Text Solution

Verified by Experts

Each of the charged sphere will have potential energy due to its own charge
`U_(1)=(1)/(8piepsilon_(0))(q^(2))/(r)`
The mutual potential energy stored in one sphere in the electric field of the other is
`U_(2)=(1)/(4piepsilon_(0))(q^(2))/(R)`
Therefore the P.E. stored in the system of sphere is
`U=[2U_(1)+U_(2)]=(q^(2))/(4piepsilon_(0))[(1)/(R)+(1)/(r)]`
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