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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 The diagram below displays a typical voltage vs. time graph NNO AAO B_BO omegaomO tautaO. center includegraphicswidthcm#image_path:generator-coil-in-decreasing-field-# center
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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 The diagram below displays a typical voltage vs. time graph NNO AAO B_BO omegaomO tautaO. center includegraphicswidthcm#image_path:generator-coil-in-decreasing-field-# center
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Title Matched on
Loop in Decreasing Field tags
Rectangular Coil tags
Numerical Calculation of Magnetic Flux tags
Rotor Blades tags
Falling Ring tags

Attributes & Decorations
Branches
Magnetism
Tags
electromagnetic induction, faraday law, magnetic flux
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Algebraic
Decoration
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