A long straight cylindrical shell has inner radius $R_{i}$ and outer radius $R_{0} .$ It carries current $i$ , uniformly distributed over its cross-section. A wire is to placed parallel to the cylinder axis, in the hollow region $(r < R_{i})$

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

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

The magnetic field is zero everywhere in the hollow region $(r < R_{i}) .$ We conclude that wire does not carry any current

The magnetic field is zero everywhere outside the shell $(r > R_{0}) .$ We conclude that the wire is on the cylinder axis and carries $i$ in the direction opposite to the direction of current in the shell

answer is B, D.

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Detailed Solution

Use Ampere’s circuital law.

$\int B . d l = μ_{0} . I_{e n c l o s e d}$

Magnetic field will be zero when enclosed current is zero.

In the hollow region, enclosed current is zero, if the wire does not carry any current.

Outside the shell, enclosed current will be zero when the wire is carrying equal current in the opposite direction to that of the current in the shell and is along the cylinder axis.

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