The inductance of a closely wound coil is such that an emf of 3.0 mV is induced when the current

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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 $3.0 \mathrm{mV}$ is induced when the current changes at the rate of $5.0 \mathrm{~A} / \mathrm{s}$. A steady current of $8.0 \mathrm{~A}$ produces a magnetic flux of $40 \mu$ Wb through each turn. (a) Calculate the inductance of the coil. (b) How many turns does the coil have?

Key Concepts

Inductance

Inductance is a property of an electrical conductor by which a change in current flowing through it induces an electromotive force (emf) in itself and in nearby conductors. It is measured in henries (H) and quantifies the ability to store energy in a magnetic field generated by the current. The larger the inductance, the greater the emf produced by a given rate of change of current.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an emf in the circuit. When applied to a coil, this law shows that the induced emf is proportional to the rate of change of current through the coil and the coil’s inductance, commonly expressed as emf = -L (dI/dt). This principle is fundamental in calculating inductance based on a known change in current and the resulting induced voltage.

Magnetic Flux Linkage

Magnetic flux linkage is the product of the number of turns in a coil and the magnetic flux through each turn. It represents the total magnetic coupling of the coil and is crucial in understanding energy storage in magnetic fields. The induced emf in a coil is also related to the change in this magnetic flux linkage over time.

Relationship between Coil Parameters and Number of Turns

The number of turns in a coil affects both the magnetic flux linkage and the total inductance. In a coil, the total flux linkage is the sum of the flux through each individual turn. By relating the magnetic flux through one turn to the current and the overall inductance, one can determine the number of turns. This provides a connection between the physical construction of the coil and its electrical behavior.

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