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Misconception of motional EMF?

  1. Dec 19, 2014 #1
    For motional EMF:

    $$ \epsilon = -vBL$$

    If a conductor moves in a constant magnetic field, there isn't induced EMF correct? Only when existing/entering the field there is induced EMF?
    I've had this misconception, that any motion(fast/slow) in a magnetic field would instantly induced EMF, but I think that's wrong @jim hardy made me realize this from my older post.
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  3. Dec 19, 2014 #2


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    some one will correct me if I am wrong ;)

    If the wire is crossing magnetic field lines you will get an induced current in the wire
    if the wire is moving parallel to the field lines, there will be no induced current

  4. Dec 19, 2014 #3

    jim hardy

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    I remember that thought experiment.... the post was titled
    Induced current of this conductor?
    Maybe you'd put the sketch back up....

    to induce Current requires there be a closed loop.
    to induce EMF does not.

    A single conductor moving through a magnetic field will have a voltage induced in a direction that is perpendicular to both B, and v in the amount BLv.
    That word "perpendicular" is more important than it looks.

    That voltage comes about because of Lorentz force QV cross B. V and B are vectors.

    In that post you refer to, we went ahead and closed the loop so current could flow.

    I found a sketch here that might help: http://www.asiaman.net/androo/academics/TAing/phys24/week1/ [Broken]

    http://www.asiaman.net/androo/resources/academics/phys24/figures/ClosedLoop-v1-fig1a.png [Broken] θ

    B is going into the paper.
    v is to the right.
    v cross B points up.
    What is the direction of voltage induced in each conductor?
    Left vertical conductor will see its internal free charges pushed up , making BLv volts between its ends, i think positive at top.
    both horizontal conductors will see their internal free charges pushed up. making B X(thickness of wire) X v volts between top and bottom surfaces of the conductor, but no voltage between their ends because v cross B points up
    Right vertical conductor will have no induced voltage because it is outside the field.

    So, what's the sum of the voltages induced in the whole closed loop? The BLv in left wire. Current can flow.

    I think if you check up, that formula E = BLv requires mutual perpendicularity.
    To account for non-perpendicularity we should multiply by sin(the non-perpendicularangle)
    In those horizontal wires, their L and v are not perpendicular they're in same direction. If you multiply by sin(0) you get the correct end to end voltage for them, zero.

    Here's another link that at least mentions nonperpendicularity.. when it describes closed loop of a generator see section 22.7

    I like to make my mental model and equations agree by at least two different thought trains.

    Some people work induction problems by "Flux Cutting", as above where we figured the voltage for each wire in our closed loop as it is "cut" by lines of flux..
    Others prefer "Flux Linking" where one calculates the flux enclosed by the loop and its rate of change.
    That ohio-state link shows both. methods.
    In your loop, enclosed flux is BLx , rate of change of flux is BLdx/dt = BLv, and induced voltage is that many volts per turn.

    Hope this helps.

    old jim
    Last edited by a moderator: May 7, 2017
  5. Dec 19, 2014 #4
    Try watch this video
  6. Dec 19, 2014 #5
    I was under the assumption that motion in a constant magnetic field would not induced any EMF at all since there is no form of change?
    Only at the edges, where the conductor exits/enters the field would there be any induced EMF?
  7. Dec 19, 2014 #6

    jim hardy

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    The whole is equal to the sum of its parts.

    Are you assuming a loop or a straight wire? Motion at what angle relative to field?

    QV cross B for a wire and ndΦ/dt for a loop are where i always start my thinking.

    It's not easy to train our mind to think simple, we want to jump straight to the answer.
    Only after we get the necessary thought steps imprinted as a habit do they become easy.

    Remember the uncertainty (and scraped elbows) from your first bicycle....

    That's true for a loop that's not rotating. But it's not a general statement. Back to basics: ∑BLvsinθ 's
  8. Dec 19, 2014 #7
    Im assuming this to be a wire, it makes sense that for a wire it would have induced EMF but for a loop, it would cancel out when moving in a magnetic field.
  9. Dec 19, 2014 #8
    @jim hardy Although the loops cancels the voltages, if it we're connected to a circuit it does not correct? They wires that cancel out in a loop would act as if two voltage sources in parallel?
  10. Dec 19, 2014 #9

    jim hardy

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    Those words sure do sound right. I hope the picture behind them in your brain is the same as the one they painted in my brain !

    Einstein said ,in response to being asked how scientists think;
    So we have this picture in our brain, we translate it to words and hope the words paint a similar picture in the brain of the person receiving them
    That's why i like math it is less ambiguous than words.
    But math seems to enjoy torturing me.... so i have to build mental models that make the math intuitive.

    How i envy people who can think in equations !

    old jim

    Equal voltages in parallel if equal will oppose one another , so no current will circulate between them.
  11. Dec 19, 2014 #10

    jim hardy

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    If both are in the uniform magnetic field, yes.. Parallel voltages that are equal won't circulate current between themselves. One would have to win the tug-of-war.

    If they're connected also to a circuit by wires that don't have voltage induced in them, or at least enough voltage to stop current, current will flow.
  12. Dec 19, 2014 #11
  13. Dec 19, 2014 #12

    jim hardy

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    Thank you for the kind words !

    I often quote Lavoisier who wrote "Science is but language well arranged."

    You might enjoy his "Introduction to Treatise on Chemistry" .
    Especially the last few paragraphs.
    Here's a sample from early in the essay::

    I do countless thought experiments to see whether my latest 'assumptions' are truth or self-deceit. If they lead me to a known equation, well that's good, if they lead me to a conflict with known facts then that must be resolved. Gives me something to do in those periods of mental vacuum like while i'm raking leaves or the TV is on .

    Have fun . Use your daydreams to test and adjust your mental models of physical processes.

    old jim
    Last edited: Dec 19, 2014
  14. Dec 19, 2014 #13


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    Thanks Jim, that was the bit I didn't clarify :)

    refer to your quote in my signature haha
  15. Dec 21, 2014 #14
    Jim, how important is the direction of magnetic field to induced EMF? Velocity and the magnetic field's direction will determine the induced current's direction?
    I assumed it velocity would be the most important. Forgot about how magnetic field's direction might have an influence.
  16. Dec 21, 2014 #15
    Ow I remember from this.
  17. Dec 21, 2014 #16
    Very important. Do you know how to read/interpret this formula?:
    If you don't, people in PF math subsection can help you to clear doubts about cross and dot vector products.
  18. Dec 21, 2014 #17
    Yes, I realized the cross product between the velocity and the magnetic field.
    But can't explain why in terms of the math.
    Last edited: Dec 21, 2014
  19. Dec 21, 2014 #18


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    The Maths only describes the relationship. It isn't really an explanation. But then again, there are very few real explanations in Science - it's just putting things in the context of things we are already familiar with.
  20. Dec 22, 2014 #19
    In this case we must take into consideration the electrons in the conductor

    While moving in the magnetic field the electrons will face a force pulling them to one end thus creating a potential difference due to motion of these electrons
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