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https://texercises.com/exercise/generator-coil-in-variable-field/
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Exercise:
A generator coil rotates in a magnetic field that decreases exponentially. Derive a formal expression for the voltage induced in the coil. Discuss the physical meaning of the parameters.

Solution:
The flux through the coil as a function of time is given by the expression Phi_m N A Btsinomega t N A B_ e^-t/tau sinomega t The induced emf is the derivate of the flux: mathcalEt -dotPhi_mt N A B_lefte^-t/taufrac-tausinomega t+e^-t/taucosomega tomegaright N A B_e^-t/tauleftcosomega tomega-fracsinomega ttauright The parameters are: itemize item N: number of turns item A: area of coil item B_: initial strength of magnetic field item omega: angular frequency of rotation item tau: time constant for exponential decay itemize
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Exercise:
A generator coil rotates in a magnetic field that decreases exponentially. Derive a formal expression for the voltage induced in the coil. Discuss the physical meaning of the parameters.

Solution:
The flux through the coil as a function of time is given by the expression Phi_m N A Btsinomega t N A B_ e^-t/tau sinomega t The induced emf is the derivate of the flux: mathcalEt -dotPhi_mt N A B_lefte^-t/taufrac-tausinomega t+e^-t/taucosomega tomegaright N A B_e^-t/tauleftcosomega tomega-fracsinomega ttauright The parameters are: itemize item N: number of turns item A: area of coil item B_: initial strength of magnetic field item omega: angular frequency of rotation item tau: time constant for exponential decay itemize
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Branches
Magnetism
Tags
electromagnetic induction, faraday law, magnetic flux
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Algebraic
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