Faraday's Law of Electromagnetic Induction

In summary, we discussed a scenario where a constant magnetic field of 2.26 T and an angle of 66.0° passes through a rectangular loop with dimensions 0.348 m x 0.593 m. We calculated the average emf induced in the loop when the magnetic field decreased to zero in 0.475 s, giving a value of 3.99*10^-1 V. For the second part, we explored the magnitude of the rate at which the area should change in order to maintain the same average emf if the magnetic field remained constant. Using the equation e=-Bcos(66°)(dA/dt), we found that the change in area with respect to time is equal to the
  • #1
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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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  • #2
[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.
 
  • #3
(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:
  • #4
[itex] d\Phi =\vec{B}\cdot\vec{n} dA=B\cos 66deg \ dA [/tex]

Divide through "-dt"...
[tex] e=-B\cos 66deg \ \frac{dA}{dt} [/tex]

And now express [itex] \vec{dA}{dt} [/itex] as a function of B,e,cos 66°...

Daniel.
 

Related to Faraday's Law of Electromagnetic Induction

1. What is Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction is a basic law of electromagnetism that explains the relationship between electric circuits and magnetic fields. It states that a changing magnetic field can induce an electric current in a nearby circuit, and vice versa.

2. Who discovered Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction is named after the English scientist Michael Faraday, who first discovered it in the early 19th century. He conducted various experiments with magnets and coils and observed the phenomenon of electromagnetic induction.

3. How is Faraday's Law of Electromagnetic Induction used in everyday life?

Faraday's Law of Electromagnetic Induction is used in many modern technologies, such as generators, transformers, and electric motors. These devices work by utilizing the principle of electromagnetic induction to produce and control electric currents.

4. What is the mathematical equation for Faraday's Law of Electromagnetic Induction?

The mathematical equation for Faraday's Law of Electromagnetic Induction is:
EMF = -N(dΦ/dt)
where EMF is the electromotive force (voltage), N is the number of turns in the coil, and (dΦ/dt) is the rate of change of the magnetic flux through the coil.

5. What factors can affect the strength of the induced current in Faraday's Law of Electromagnetic Induction?

The strength of the induced current in Faraday's Law of Electromagnetic Induction can be affected by the strength of the magnetic field, the rate of change of the magnetic field, and the number of turns in the coil. Additionally, the resistance of the circuit and the properties of the materials used can also impact the induced current.

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