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Question

A current is flowing through a thin cylindrical shell of radius R. If energy density in the medium, due to magnetic field, at a distance r from axis of the shell is equal to U then which of the following graphs is correct

A
a
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B
b
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C
c
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D
d
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Solution

The correct option is B b
When a current flows through cylindrical shell, then according to Ampere circuital law, magnetic induction inside it will be equal to zero. Hence energy density at r < R is equal to zero.
Therefore, (a), (c) and (d) are wrong.
When r > R, B=μ0i2πr.
Since U=B22μ0, therefore, outside the shell, U=μ0i28π2r2. It means, just outside the shell, U=μ0i28π2R2 and when r, U0.
Hence (b) is correct.

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