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

A $0.45-\mathrm{T}$ magnetic field is perpendicular to a circular coil of wire with 53 loops 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 in the coil? 56. Figure $23.25$ shows the magnetic flux through a wire loop as a function of time. What is the induced emf in the loop at (a) $t=0.050 \mathrm{~s}$, (b) $t=0.15 \mathrm{~s}$, and (c) $t=0.50 \mathrm{~s}$ ?

A $0.45-\mathrm{T}$ magnetic field is perpendicular to a circular coil of wire with 53 loops 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 in the coil?
56. Figure $23.25$ shows the magnetic flux through a wire loop as a function of time. What is the induced emf in the loop at (a) $t=0.050 \mathrm{~s}$, (b) $t=0.15 \mathrm{~s}$, and (c) $t=0.50 \mathrm{~s}$ ?

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Key Concepts

Faraday's Law of Electromagnetic Induction

This law states that an electromotive force (emf) is induced in a circuit when there is a change in magnetic flux through the circuit. The magnitude of the induced emf is proportional to the rate at which the magnetic flux changes with time. It is mathematically represented as emf = -d?/dt, where the negative sign indicates the direction of the induced emf (as given by Lenz's law).

Magnetic Flux

Magnetic flux is defined as the product of the magnetic field strength and the area through which the field lines pass, taking into account the angle between the field and the area's normal. It is a measure of the total magnetic field penetrating a surface and is crucial when calculating the induced emf as changes in flux result in voltage generation in the coil.

Coil Geometry and Multiple Turns

The characteristics of the coil, specifically the area of each loop and the number of loops, directly affect the total magnetic flux and the resulting induced emf. When a coil has several loops, the total induced emf is the sum of the emf produced in each loop. Thus, a coil with multiple turns multiplies the effect of the changing magnetic flux, enhancing the overall induced emf.

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