Understanding Faraday's Law: Solving for Induced EMF in a Uniform Magnetic Field

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SUMMARY

This discussion focuses on applying Faraday's Law to determine the rate of change of the radius of a circular loop in a uniform magnetic field to achieve zero induced electromotive force (emf). The loop has a radius of 12 cm and is subjected to a magnetic field of 0.5 T, which decreases at a rate of -0.01 T/s. The initial emf calculated is 0.01 V, and the initial magnetic flux is 0.0023 Wb. The solution requires balancing the rate of change of the magnetic field with the change in the loop's radius to cancel the induced emf.

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  • Knowledge of magnetic flux and its calculation
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  • Basic calculus for solving rates of change
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Homework Statement


A circular loop of radius r = 12cm is in a uniform magnetic field B=.5T w/ its plane normal to the direction of the field. If the magnitude of B then decreases at a constant rate of -.01T/s, at rate should r increase so the induced emf in the loop is zero?


Homework Equations


Faraday's Law


The Attempt at a Solution


The question gives the initial emf in the loop = .01V and you can solve for the initial flux =.0023Wb. From here I don't know what to do.
 
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If both the radius and the field are changing, what is the formula for the induced emf?

HINT:

You should have two terms in your equation, one involving the rate of change of B and one involving the change in r. You then want to pick a value for the rate of change of r such that both terms cancel.
 

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