Cross-section of an infinite cylinder is shown. A current I uniformly distributed over its cross-section is flowing along its length. Now a cylindrical cavity of radius R/2,whose axis is parallel to the axis of the cylinder, is formed inside it. Then

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magnetic fields at the centres of both cylinders is same in magnitude but opposite in direction

magnetic field at the centre of both cylinders is opposite in direction and unequal in magnitude

magnetic fields at the centres of both cylinders is same both in magnitude and direction

magnetic fields at the centres of both cylinders is same in direction but unequal in magnitude

answer is A.

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Detailed Solution

In a cylindrical cavity like this, magnetic field is uniform and perpendicular to the line joining the centres of the cylinder and directed in the same direction. Magnitude of field at the centre of the cylinder as well as at the center of the cavity is $\frac{μ_{0} I}{4 π R} .$ i.e., same both in magnitude and direction.

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