Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon (a) the rates at which currents are changing in the two coils (b) relative position and orientation of the two coils (c) the currents in the two coils (d) the materials of the wires of the coils

Answer: (b). M depends only on geometry: number of turns, sizes, separation, relative orientation and the core medium. It does not depend on the currents, their rates of change, or the wire material. So the answer is (b) relative position and orientation of the two coils.

Two coils are placed close to each other. The mutual inductance of… | JEE Main 2003 (AIEEE)

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Mutual Inductance

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

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Answer: (b)

$M$ depends only on geometry: number of turns, sizes, separation, relative orientation and the core medium.
It does not depend on the currents, their rates of change, or the wire material.
So the answer is (b) relative position and orientation of the two coils.

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