The inductance of a closely wound coil is such that an emf of 3.00 mV is induced when the curren

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The inductance of a closely wound coil is such that an emf...

The inductance of a closely wound coil is such that an emf of 3.00 $\mathrm{mV}$ is induced when the current changes at the rate of 5.00 A/s. A steady current of 8.00 A produces a magnetic flux of 40.0 $\mu \mathrm{Wb}$ through each turn. (a) Calculate the inductance of the coil. (b) How many turns does the coil have?

The inductance of a closely wound coil is such that an emf of
3.00 $\mathrm{mV}$ is induced when the current changes at the rate of 5.00
A/s. A steady current of 8.00 A produces a magnetic flux of 40.0
$\mu \mathrm{Wb}$ through each turn. (a) Calculate the inductance of the coil.
(b) How many turns does the coil have?

Key Concepts

Flux Linkage

Flux linkage refers to the total magnetic flux that is linked (or 'enclosed') by all the turns of a coil. For a coil with multiple turns, the total flux linkage is the product of the magnetic flux per turn and the number of turns, and it plays an important role in calculating the inductance and the induced emf based on the rate of change of current.

Rate of Change of Current

The rate of change of current (di/dt) indicates how quickly the current is changing with respect to time. In circuits containing inductors, this changing current results in a time-varying magnetic field which, according to Faraday’s law, induces an emf that opposes the change in current. This concept is pivotal in understanding the transient behavior of inductive circuits.

Magnetic Flux

Magnetic flux represents the total magnetic field passing through a given area, such as a loop of a coil. It is a measure of the quantity of magnetism, taking into account the field strength and the area through which it spreads, and is measured in webers (Wb). Magnetic flux is crucial in determining the flux linkage in coils, which in turn is related to the inductance.

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic field, either due to the motion of a magnet or a varying current in a coil, induces an electromotive force (emf) in a conductor. This phenomenon is governed by Faraday's law and is fundamental to the operation of transformers, inductors, and generators.

Inductance

Inductance is a property of an electrical circuit, usually in a coil, that quantifies its ability to store energy in a magnetic field when electric current flows through it. It is defined as the ratio of the magnetic flux linkage to the current producing it, and is measured in henries (H). This concept is central in analyzing circuits where changes in current produce opposing electromotive forces (emfs).

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