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

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To solve for the induced EMF in a circular loop when the magnetic field decreases, both the change in magnetic field (B) and the radius (r) must be considered. The initial EMF is given as 0.01V, with the initial magnetic flux calculated at 0.0023 Wb. The problem requires finding a rate of change for the radius that will result in a zero induced EMF, which involves balancing the effects of the changing magnetic field and the changing radius. The solution involves applying Faraday's Law, which states that the induced EMF is proportional to the rate of change of magnetic flux. Ultimately, the goal is to determine a specific rate of change for r that cancels the induced EMF from the changing B.
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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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