What area must a 27-loop coil have if it is to produce a...

What area must a 27-loop coil have if it is to produce a maximum emf of $22 \mathrm{~V}$ when rotating in a magnetic field of $0.82 \mathrm{~T}$ with an angular speed of $290 \mathrm{rad} / \mathrm{s}$ ?

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Key Concepts

Faraday's Law of Electromagnetic Induction

This fundamental principle states that a change in magnetic flux through a circuit induces an electromotive force (EMF) across it. It is the cornerstone for understanding how generators convert mechanical motion into electrical energy by changing the magnetic environment of coils.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a given area. It is directly related to the induced EMF in a coil, as variations in the flux—caused by changes in the magnetic field, the coil’s area, or its orientation—result in an induced voltage.

Rotating Coil in a Magnetic Field

When a coil rotates in a magnetic field, it experiences a time-varying magnetic flux, leading to an alternating induced EMF. The maximum EMF is achieved when the rate of change of flux is greatest, which depends on factors such as the coil’s area, the strength of the magnetic field, the number of loops, and the angular speed.

Angular Motion and EMF Generation

The angular speed of a rotating coil determines how quickly its orientation with respect to the magnetic field changes, affecting the rate at which the magnetic flux varies. A higher angular speed leads to a more rapid change in flux and, consequently, a higher induced EMF according to Faraday’s Law.

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