Induced EMF and a circular loop of wire

In summary: Thanks for the help. sorry cannot get fraction in latex to work, I am a newb.V = -\frac{d}{dt}[BA] = -[\frac{BA_f - BA_i}{t_f - t_i}]
  • #1
anonymousphys
29
0

Homework Statement


A 25-turn circular loop of wire has a diameter of 1m. In 0.2 seconds it is flipped 180 degrees at a location where the magnitude of the Earth's magnetic field is 50 micro T. What is the emf generated in the loop?

Homework Equations


-(dB/dt)(A)=V

The Attempt at a Solution


When I use NABwsin(wt)=V, I get zero. When I use -(dB/dt)(A)=V, I get a non-zero number. I believe the 2nd equation works but why doesn't the first work?

Thanks for any help.
 
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  • #2
anonymousphys said:

Homework Statement


A 25-turn circular loop of wire has a diameter of 1m. In 0.2 seconds it is flipped 180 degrees at a location where the magnitude of the Earth's magnetic field is 50 micro T. What is the emf generated in the loop?


Homework Equations


-(dB/dt)(A)=V


The Attempt at a Solution


When I use NABwsin(wt)=V, I get zero. When I use -(dB/dt)(A)=V, I get a non-zero number. I believe the 2nd equation works but why doesn't the first work?

Thanks for any help.

Where does the first equation come from? If you used d/dt[BA] = V is B changing?
 
  • #3
Thanks for the reply. NABwsin(wt)=V comes from taking the derivative of NABcos(wt)=magnetic flux. The 2nd equation should be taking into account the change in angle. Shouldn't both equations lead to the same answer?
 
  • #4
anonymousphys said:
Thanks for the reply. NABwsin(wt)=V comes from taking the derivative of NABcos(wt)=magnetic flux. The 2nd equation should be taking into account the change in angle. Shouldn't both equations lead to the same answer?

I believe they should. How did you get 0 for the first equation? I do not get 0.
 
  • #5
Show the work on both because when I use the 2nd equation all that happens is I derive the first equation.
 
  • #6
zachzach said:
I believe they should. How did you get 0 for the first equation? I do not get 0.

w=pi/(.2)
sin(wt) when t=(.2) equals 0.

Hm..I think I'm not using the equation correctly?
 
  • #7
Doh! I see what you mean :/.
 
  • #8
Here's my thoughts: By plugging in wt only for the final time, you only are calculating the emf produced at that instant. So maybe you should use:

V = -d/dt(BA) = -[BA(Final) - BA(Initial)]/[t(Final) - t(Initial)]

sorry cannot get fraction in latex to work, I am a newb.
 
Last edited:
  • #9
[tex]

V = -\frac{d}{dt}[BA] = -[\frac{BA_f - BA_i}{t_f - t_i}]

[/tex]

I did it in latex :).
 

1. What is induced EMF?

Induced EMF, or electromotive force, is the voltage generated in a conductor when it is moved through a magnetic field or when there is a change in the magnetic field passing through the conductor.

2. How is induced EMF related to a circular loop of wire?

A circular loop of wire is a conductor that can be moved through a magnetic field, or have a magnetic field pass through it, causing induced EMF to be generated in the wire.

3. What factors affect the magnitude of induced EMF in a circular loop of wire?

The magnitude of induced EMF in a circular loop of wire is affected by the strength of the magnetic field, the speed at which the loop is moved through the field, and the number of turns in the wire loop.

4. What is Faraday's Law and how is it related to induced EMF?

Faraday's Law states that the magnitude of the induced EMF is proportional to the rate of change of the magnetic flux through the loop. This means that the faster the magnetic field changes or the more the loop moves through the field, the greater the induced EMF will be.

5. How is induced EMF used in practical applications?

Induced EMF is used in a variety of practical applications, such as generators, transformers, and electric motors. It is also used in technologies like wireless charging, where induced EMF is used to transfer energy from a source to a receiver without the need for physical contact.

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