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# Physics/Induced emf

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Question
A circular loop of one turn and radius 5 cm is positioned with its axis parallel to a magnetic field of 0.6T. Suddenly the area of the loop collapses to 0 in 0.5 ms. What emf was induced?

a. 9.4 V b. 6.7 V  c.3.4 V  d. 1.2 V  e. 11.2 V

I'm not sure of to go about this since the area is 0. I was going to use the formula: e= L(I-Io)/ t. But there also is no current. How would I go about solving this problem?

Answer
According to Faraday's Law the EMF generated in a closed conducting path is equal to the rate of change of the magnetic flux:
EMF=-Ndphi/dt  where N is the number of urns in the closed path, Dphi is the change in magnetic flux and dt is the time interval over which the change occurred.
In this case the EMF will be:
EMF=-N*dB*A/dt=-1*B*dA/dt=-1*0.6*(pi*0.05^2)/0.5x10^-3=9.42V

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#### James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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