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A charge Q is uniformly on a ring of rad...

A charge `Q` is uniformly on a ring of radius `R`. Find the electric potential on the axis of ring at distance `x` from the centre of the ring. Sketch variation of potential with respect to `x`.

Text Solution

Verified by Experts

Small potential at `P` due to `dq`
`dV = (1)/(4 pi in_(0)) .(dq)/(sqrt(R^(2) + x^(2)))`
`V_(p) = Sigma dV = (1)/(4 pi in_(0)) .(Sigma dq)/(sqrt(R^(2) + x^(2)))`
`= (1)/(4 pi in_(0)) .(Sigma dq)/(sqrt(R^(2) + x^(2)))`
At center `O , x = 0`
`V_(0) = (1)/( 4 pi in_(0)) .(Q)/(R )`
`V v//s x` graph :
`x = 0 , V_(0) = (1)/( 4 pi in_(0)) .(Q)/(R )`
`x = x , V = (1)/(4 pi in_(0)) .(Q)/(sqrt(R^(2) + x^(2)))`
`x rarr oo , V rarr 0`

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Knowledge Check

  • A charge of 5 nC is uniformly distributed on a ring of radius 4 cm. Find the potential at the axis at a distance of 3 cm from the center.

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