Induced Voltage Equation: Solving for Constant Magnetic Field

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Discussion Overview

The discussion revolves around the calculation of induced voltage in a circular loop subjected to a changing magnetic field, specifically using Faraday's law of electromagnetic induction. Participants explore the implications of a magnetic field increasing at a constant rate and the associated calculations required to determine the induced emf.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants express confusion regarding the application of Faraday's law when the magnetic field is the only variable changing, questioning the correct formulation of the induced voltage equation.
  • One participant describes a specific scenario involving a circular loop in a magnetic field of 0.3 T, which is increased by a factor of 2.4 over 13 seconds, and attempts various calculations for induced emf.
  • Several participants seek clarification on the initial and final values of the magnetic field, emphasizing the importance of understanding the factor by which the field is increasing.
  • Discussions arise about the interpretation of the problem statement, particularly regarding the time frame and the meaning of "increased by a factor of 2.4."
  • Participants share their calculations and results, with some expressing uncertainty about their answers and the methodology used.
  • One participant highlights the need to consider the change in magnetic field over time rather than just the final field value in their calculations.
  • Another participant mentions the second part of the problem, which involves calculating average induced voltage when the loop is removed from the magnetic field region.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the correct interpretation of the problem statement and the calculations involved. There are multiple competing views on how to approach the problem, and confusion persists regarding the application of Faraday's law in this context.

Contextual Notes

Some participants express uncertainty about the wording of the problem and its implications for the calculations. There are unresolved questions about the definitions of initial and final magnetic fields and how they relate to the induced voltage.

Who May Find This Useful

This discussion may be useful for students or individuals studying electromagnetism, particularly those interested in the application of Faraday's law and the calculation of induced voltage in varying magnetic fields.

laxmaster08
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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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laxmaster08 said:
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?
 
Doc Al said:
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 I've tried [(2.4-0.3)/13)*pi(.31)^2], [(2.4+0.3)/13)*A], and [(2.4/13)*A]. All in magnitude form.
 
Last edited:
laxmaster08 said:
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?
 
Doc Al said:
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
 
laxmaster08 said:
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?
 
doc al said:
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
 
laxmaster08 said:
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?
 
Doc Al said:
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
laxmaster08 said:
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
Doc Al said:
Nope. Reread my last comment.

Ok so I am going to multiply my initial 0.3 by a factor of 2.4?
 
  • #12
*over a time period of 13s
 
  • #13
laxmaster08 said:
Ok so I am going to multiply my initial 0.3 by a factor of 2.4?
Yes. At least I hope so!
 
  • #14
nope
 
  • #15
Any ideas? Faraday doesn't say anything about resistance so I'm guessing that pertains to part b of the problem...
 
  • #16
laxmaster08 said:
nope
Nope what?
 
  • #17
Doc Al said:
Nope what?

That doesn't work.
 
  • #18
laxmaster08 said:
That doesn't work.
Show what you did.
 
  • #19
Doc Al said:
Show what you did.

(2.4*0.3)/13)*pi*(.31)^2=0.0167V
 
  • #20
laxmaster08 said:
(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
Doc Al said:
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
laxmaster08 said:
Success! That problem had really sneaky wording.
Finally! :cool:
 
  • #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"
 
  • #26
Haha yah that took quite a while. If your out ill understand I can probably figure this one out...probably.
 
  • #27
What does it mean by pulled out of the magnetic field? Does that mean a force due to current in the loop is pushing it?
 
  • #28
Will this use Faraday's?
 
  • #29
Nvm that was cake! thanks man peace out
 

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