A certain clastic conducting material is stretched into a...

A certain clastic conducting material is stretched into a circular loop of 12.0 $\mathrm{cm}$ radius. It is placed with its plane perpendicular to a uniform 0.800 $\mathrm{T}$ magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 $\mathrm{cm} / \mathrm{s} .$ What emf is induced in the loop at that instant?

A certain clastic conducting material is stretched into a circular loop of 12.0 $\mathrm{cm}$ radius. It is placed with its plane perpendicular to a uniform 0.800 $\mathrm{T}$ magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of
75.0 $\mathrm{cm} / \mathrm{s} .$ What emf is induced in the loop at that instant?

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Key Concepts

Rate of Change of Area

When a conductor such as a loop changes its shape or size over time, its enclosed area changes. The rate at which this area changes, dA/dt, directly affects the rate of change of the magnetic flux through the loop in a constant magnetic field and thus determines the magnitude of the induced emf according to Faraday's Law.

Faraday’s Law of Electuction

This fundamental principle of electromagnetism states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in that loop. It is expressed mathematically as emf = -d?/dt, where ? represents the magnetic flux, and the negative sign reflects Lenz's Law, indicating that the induced emf opposes the change in flux.

Magnetic Flux

Magnetic flux is a measure of the amount of magnetic field passing through a given area. For a uniform magnetic field perpendicular to the surface, it is calculated as ? = B·A, where B is the magnetic field strength and A is the area of the loop. Changes in the flux, whether due to changes in the magnetic field or the area of the loop, are central to the process of electromagnetic induction.

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