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Question

# A solid cylinderical wire of radius 'R' carries a current T. The magnetic field is 5μT at a point, Whaich is '2R' distance away from the axis of wire. Magnetic field at a point which is R/3 distance inside from the surface of the wire is :-

A
103μT
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B
203μT
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C
53μT
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D
403μT
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Solution

## The correct option is B 203μTGiven:- wire of radius=R Curret=T The magnetic field=5uT (At a distance 2R)To find:- Magnetic field at a point which is R/3 distance inside from the surface of the wireSolution:- In solid cylindrical conductor; r>R then, B= μ0I2πR So B at 2R from axis SμT= μ0I2π(2R) ⇒SμT=μ0I4πR ............(1) Now we have to take from the axis of cylinder. So, r = R- R3=2R3 B′=μ0I2 = μ0Ir2πR2 = μ0I(2R3)2πR2 B′=2μ0I6πR .............(2) Divide equation 1 by equation 2 SμTB′=μ0I4πR2μ0I6πR ⇒SμTB′=34 ∴B′=203μ0T Hence the correct option is B

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