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Q.

A long straight cylindrical shell has inner radius Ri and outer radius Ro. It carries current i, uniformly distributed over its cross section. A wire is to be placed parallel to the cylinder axis, in the hollow region .

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a

The magnetic field is zero everywhere in the hollow region. We conclude that the wire may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell

b

The magnetic field is zero everywhere in the hollow region (r<Ri) We conclude that the wire is on the cylinder axis and carries current i in the same direction as the current in the shell.

c

The magnetic field is zero everywhere in the hollow region. We conclude that the wire does not carry any current

d

The magnetic field is zero everywhere outside the shell (r>R0) We conclude that the wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell.

answer is B, D.

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Detailed Solution

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Applying Ampere's Law,

B2πr=μ0ienclosed ienclosed=0 B=0

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A long straight cylindrical shell has inner radius Ri and outer radius Ro. It carries current i, uniformly distributed over its cross section. A wire is to be placed parallel to the cylinder axis, in the hollow region .