A 0.45-T magnetic field is perpendicular to a circular loop...

A 0.45-T magnetic field is perpendicular to a circular loop of wire with 53 turns and a radius of $15 \mathrm{cm} .$ If the magnetic field is reduced to zero in $0.12 \mathrm{s}$, what is the magnitude of the induced emf?

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Key Concepts

Effect of Multiple Turns

When a coil has multiple turns, each loop experiences the same change in magnetic flux. The total induced emf is the sum of the contributions from all individual loops. Therefore, the net emf is multiplied by the number of turns in the coil, which significantly increases the overall induced voltage.

Area Calculation for Circular Loops

For a circular loop, the area through which the magnetic field passes is determined by the formula A = ?r², where r is the radius of the loop. This area is crucial for calculating the magnetic flux, thereby directly affecting the induced emf in the circuit.

Faraday's Law of Electromagnetic Induction

This law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit. It is expressed mathematically as emf = -N (??/?t), where N is the number of turns in the coil and ??/?t is the rate of change of magnetic flux. The negative sign indicates the direction of the induced emf, as described by Lenz's law.

Magnetic Flux

Magnetic flux represents the amount of magnetic field passing through a given area, and is calculated by the product of the magnetic field strength and the area perpendicular to the field. It is an essential concept in electromagnetic induction as the change in magnetic flux results in the induction of an emf.

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