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Question

# A ring of radius R is made out of a thin metallic wire of area of cross section A. The ring has a uniform charge Q distributed on it. A charge q0 is placed at the centre of the ring. If Y is the young`s modules for the material of the ring and ΔR is the change is the radius of the ring then find ΔR.

A
q0Q8π2ε0RAY
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B
q0Q8π2ε20RAY
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C
q0Q4π2ε0RAY
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D
q0Q4πε0RAY
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Solution

## The correct option is A q0Q8π2ε0RAYFor a ring, Linear charge density λ=Q2πR Tension force in the ring T=q0λ4πε0R=q0Q8π2ε0R2 But, Young's modulus Y=StressStrain=(TA)(ΔRR)⇒ΔR=TRAY ΔR=q0QR8π2ε0R2AY ΔR=q0Q8π2ε0RAY Hence, option (a) is the correct answer.

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