Faraday's Law of Induction and wire loop

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SUMMARY

The discussion centers on calculating the average induced electromotive force (emf) in a wire loop using Faraday's Law of Induction. A wire loop with a radius of 0.3m is subjected to a magnetic field that changes from 0.30 T to 0.20 T over 1.5 seconds. The average induced emf is calculated using the formula εavg = -ΔΦB/Δt, resulting in an incorrect initial answer of -0.14135 V, later corrected to 94 mV due to arithmetic errors in the calculations.

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  • Understanding of Faraday's Law of Induction
  • Knowledge of magnetic flux (ΦB) and its calculation
  • Familiarity with the concept of induced emf
  • Basic proficiency in algebra for solving equations
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  • Study the applications of Faraday's Law in electromagnetic devices
  • Learn about the relationship between magnetic fields and electric currents
  • Explore advanced topics in electromagnetic induction, such as Lenz's Law
  • Investigate practical experiments demonstrating induced emf in wire loops
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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??
 
Last edited:
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Nvm, I found my mistakes. Just some arithmetic errors
 

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