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Question

# The given two fixed rings of radius R lie in XY plane as shown in the figure. Linear charge density of the rings A and B varies as per the relation λ=λ0sin θ and λ=λ0cos θ respectively where θ is measured from +x axis. Distance between the centre of the two rings is r>>R.

A
Force of interaction between the two ring is 34×λ20πϵ0(Rr)4
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B
Force of interaction between the two ring is 32×λ20πϵ0(Rr)4
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C
Potential energy of interaction between the two ring is πλ20R44ϵ0r3
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D
Potential energy of interaction between the two ring is zero.
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Solution

## The correct option is C Potential energy of interaction between the two ring is πλ20R44ϵ0r3Potential energy=14πϵ0πλ20R4r3when λ=λ0cosθθ=90°and r= radius of ring BR= radius of ring A

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