Faraday's Law of Induction and wire loop

AI Thread Summary
The discussion focuses on calculating the average induced electromotive force (emf) in a wire loop due to a changing magnetic field. The wire loop has a radius of 0.3m and experiences a magnetic field that reverses direction and changes from 0.30 T to 0.20 T over 1.5 seconds. The average induced emf is calculated using Faraday's Law, resulting in an initial incorrect value of -0.14135. The participant later realizes that arithmetic errors led to the discrepancy, with the correct induced emf being 94 mV. The conversation highlights the importance of careful calculations in applying Faraday's Law of Induction.
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Homework Statement


A wire loop of radius 0.3m lies so that an external magnetic field of magnitude 0.30 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.20 T in 1.5s. Find the magnitude of the average induced emf in the loop during this time.


Homework Equations


\varepsilon_{avg} = \frac{-\Delta \Phi_{B}}{\Delta t}

\Phi_{B}=BAcos \theta

The Attempt at a Solution


A=\pi r^{2}=\pi (0.30m)^{2}= 0.09\pim^{2}

0s: \Phi_{B}=BA cos \theta =(0.30T)(0.09\pi m^{2}) = 0.0848 T*m^{2}

1.5s: \Phi = -(0.20T)(0.09\pi m^{2})= -0.05655 T*m^{2}

\varepsilon_{avg}=\frac{(-0.05655-0.0848)}{1.5s}=-0.14135

The correct answer, however, is 94 mV??
 
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Nvm, I found my mistakes. Just some arithmetic errors
 
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