Induced EMF equation

  • #1
I know the equation for emf: -dflux/dt= -dB/dt*A . In my case everything is constant accept the magnetic field and I am unable to find the equation for that. I know that is what dB is for but that simply does not work in this case.

What is the equation for induced voltage, when everything is constant accept the magnetic field.
 

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  • #2
Doc Al
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What is the equation for induced voltage, when everything is constant accept the magnetic field.
That is the equation (Faraday's law). What is the exact problem?
 
  • #3
That is the equation (Faraday's law). What is the exact problem?
A circular loop of radius 31 cm is located in the plane of the paper inside a homogeneous magnetic field of 0.3 T pointing into the paper. It is connected in series with a resistor of 289 Ω. The magnetic field is now increased at a constant rate by a factor of 2.4 in 13 s. Calculate the magnitude of the induced emf in the loop during that time.

I have been using Faraday's. So far Ive tried [(2.4-0.3)/13)*pi(.31)^2], [(2.4+0.3)/13)*A], and [(2.4/13)*A]. All in magnitude form.
 
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  • #4
Doc Al
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The magnetic field is now increased at a constant rate by a factor of 2.4 in 13 s.
What's the initial magnetic field before it starts increasing? What's the final magnetic field after 13 seconds? The change in magnetic field during that time?
 
  • #5
What's the initial magnetic field before it starts increasing? What's the final magnetic field after 13 seconds? The change in magnetic field during that time?
2.4-0.3=2.1
According to Faraday this divided by the time ,t=13s, all multiplied by the area, A=pi*(.31)^2, should equal the EMF but LON-CAPA does not agree.
Am I missing something? it seems pretty straight forward but it isn't coming out right. btw my answer was 0.0488V
 
  • #6
Doc Al
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2.4-0.3=2.1
According to Faraday this divided by the time ,t=13s, all multiplied by the area, A=pi*(.31)^2, should equal the EMF but LON-CAPA does not agree.
Am I missing something? it seems pretty straight forward but it isn't coming out right. btw my answer was 0.0488V
You are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?
 
  • #7
you are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?
2.7 ill see if it works
 
  • #8
Doc Al
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2.7 ill see if it works
No. Show how you made that calculation.

FYI: Factor means multiply. If you start out weighing 150 lbs and your weight increases by a factor of 2, what's your final weight?
 
  • #9
You are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?
Ok that didnt work. So the way its worded it looks like the total time it takes to charge up 2.4 is 13s but I guess it could mean that it charges up 2.4 every second for 13s....Ill try it
 
  • #10
Doc Al
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Ok that didnt work. So the way its worded it looks like the total time it takes to charge up 2.4 is 13s but I guess it could mean that it charges up 2.4 every second for 13s....Ill try it
Nope. Reread my last comment.
 
  • #11
Nope. Reread my last comment.
Ok so im going to multiply my initial 0.3 by a factor of 2.4?
 
  • #12
*over a time period of 13s
 
  • #13
Doc Al
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Ok so im going to multiply my initial 0.3 by a factor of 2.4?
Yes. At least I hope so!
 
  • #15
Any ideas? Faraday doesn't say anything about resistance so I'm guessing that pertains to part b of the problem....
 
  • #20
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(2.4*0.3)/13)*pi*(.31)^2=0.0167V
You need the change in magnetic field over time, not just the final field.
 
  • #21
You need the change in magnetic field over time, not just the final field.
dB/dt=(2.4-0.3)/(13) ?
 
  • #22
or (2.4*0.3)-(0.3))/13
 
  • #23
Success! That problem had really sneaky wording.
 
  • #24
Doc Al
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  • #25
Now the second part looks much trickier. It looks like I will have to use right hand rule...
"Calculate the average induced voltage when the magnetic field is constant at 0.72 T while the loop is pulled horizontally out of the magnetic field region in 4.1 s"
 

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