Two coils are at fixed locations. When coil 1 has no current...

Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate $15.0 \mathrm{~A} / \mathrm{s}$, the emf in coil 1 is $25.0 \mathrm{mV}$. (a) What is their mutual inductance? (b) When coil 2 has no current and coil 1 has a current of $3.60 \mathrm{~A}$, what is the flux linkage in coil $2 ?$

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Key Concepts

Faraday's Law of Electromagnetic Induction

This principle states that an electromotive force (emf) is induced in a circuit when there is a change in magnetic flux through the circuit. The induced emf is proportional to the rate of change of the magnetic flux. It is the foundational law used to relate a time-varying current in one coil to an induced voltage in another nearby coil, which is essential for understanding problems in electromagnetic induction.

Mutual Inductance

Mutual inductance quantifies the ability of one circuit (or coil) to induce an emf in a neighboring circuit through its changing magnetic field. It depends on the geometry of the coils and their relative positions. In practical problems, the mutual inductance is determined by measuring the induced emf in one coil when the current in the other coil changes at a known rate.

Flux Linkage

Flux linkage represents the total magnetic flux that is linked with a coil, often expressed as the product of the magnetic flux and the number of turns in the coil. It is a key quantity in analyzing electromagnetic systems because any change in the flux linkage over time results in an induced emf, as described by Faraday's Law. This concept is particularly important when determining how current in one coil can influence the magnetic environment of another.

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