Faraday's Law of Electromagnetic Induction

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Homework Help Overview

The discussion revolves around Faraday's Law of Electromagnetic Induction, specifically focusing on a rectangular loop subjected to a changing magnetic field. The problem involves calculating the induced electromotive force (emf) when the magnetic field decreases to zero and exploring the relationship between the rate of change of area and the induced emf when the magnetic field remains constant.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Faraday's Law and the equations related to induced emf. There is confusion regarding the distinction between changes in magnetic field and changes in area, particularly in the context of calculating induced emf. Some participants attempt to derive relationships and express equations in different forms to clarify their understanding.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some have provided equations and attempted to clarify the relationships between variables, but there is no explicit consensus on the correct approach or resolution of confusion regarding the problem.

Contextual Notes

Participants express uncertainty about the application of equations and the transitions between different variables, indicating a need for further clarification on the concepts involved in the problem.

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A constant magnetic field passes through a single rectangular loop whose dimensions are 0.348 m x 0.593 m. The magnetic field has a magnitude of 2.26 T and is inclined at an angle of 66.0° with respect to the normal to the plane of the loop. (a) If the magnetic field decreases to zero in a time of 0.475 s, what is the magnitude of the average emf induced in the loop?
(b) If the magnetic field remains constant at its initial value of 2.26 T, what is the magnitude of the rate at which the area should change so that the average emf has the same magnitude?

I know how to figure out part a, its part b that confused me.
a) E=NAcos(theta)((B1-B2)/(t1-t2))
=3.99*10^-1 V

b) E=N(change in flux/change in time) and (change in flux)=BAcos(theta)
E=N(BAcos(theta)/(change in time))
E=NA(cos(theta))(change in B/change in time)

I think I may be going about an equation wrong, and I can't distinguish when to focus on a change in B and change in area. because I worked with B in the previous question. I dunno, I'm just confused.
 
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[tex]e=-\frac{d\Phi}{dt}[/tex]...If you have found the correct "e" at point a),the for point b),u need to compute
[tex]\frac{dA}{dt}[/tex]...

Daniel.
 
(change in A/change in time) = ((m)(m)) / (NBcos(theta))

It's not clear to me what I did wrong with this.
okay, nevermind.
V=B(change in area/change in time)
is there some special thing I am overlooking because plug and
chugging into equations I know arent helping me understand
anything.
 
Last edited:
[itex]d\Phi =\vec{B}\cdot\vec{n} dA=B\cos 66deg \ dA [/tex]<br /> <br /> Divide through "-dt"...<br /> [tex]e=-B\cos 66deg \ \frac{dA}{dt}[/tex]<br /> <br /> And now express [itex]\vec{dA}{dt}[/itex] as a function of B,e,cos 66°...<br /> <br /> Daniel.[/itex]
 

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