Misconception of motional EMF?

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.

davenn
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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

Dave

jim hardy
jim hardy
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@jim hardy made me realize this from my older post.

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]

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
http://www.physics.ohio-state.edu/~humanic/p112_lecture13.pdf

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

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PhiowPhi
Try watch this video

Stephen Tashi
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?

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....

Only at the edges, where the conductor exits/enters the field would there be any induced EMF?
That's true for a loop that's not rotating. But it's not a general statement. Back to basics: ∑BLvsinθ 's

sophiecentaur and PhiowPhi
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.

@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?

jim hardy
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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.

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;
http://www.pitt.edu/~jdnorton/Goodies/Einstein_think/index.html said:
"(A) The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be "voluntarily" reproduced and combined. There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought--before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.

(B) The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.

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.

PhiowPhi
jim hardy
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They wires that cancel out in a loop would act as if two voltage sources in parallel?

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.

PhiowPhi
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::
When we begin the study of any science, we are in a situation, respecting that science, similar to that of children; and the course by which we have to advance is precisely the same which Nature follows in the formation of their ideas. In a child, the idea is merely an effect produced by a sensation; and, in the same manner, in commencing the study of a physical science, we ought to form no idea but what is a necessary consequence, and immediate effect, of an experiment or observation.[4] Besides, he that enters upon the career of science, is in a less advantageous situation than a child who is acquiring his first ideas. To the child, Nature gives various means of rectifying any mistakes he may commit respecting the salutary or hurtful qualities of the objects which surround him. On every occasion his judgments are corrected by experience; want and pain are the necessary consequences arising from false judgment; gratification and pleasure are produced by judging aright. Under such masters, we cannot fail to become well informed; and we soon learn to reason justly, when want and pain are the necessary consequences of a contrary conduct.[5]

In the study and practice of the sciences it is quite different; the false judgments we form neither affect our existence nor our welfare; and we are not forced by any physical necessity to correct them. Imagination, on the contrary, which is ever wandering beyond the bounds of truth, joined to self-love and that self-confidence we are so apt to indulge, prompt us to draw conclusions which are not immediately derived from facts; so that we become in some measure interested in deceiving ourselves. Hence it is by no means to be wondered, that, in the science of physics in general, men have often made suppositions, instead of forming conclusions. These suppositions, handed down from one age to another, acquire additional weight from the authorities by which they are supported, till at last they are received, even by men of genius, as fundamental truths.

The only method of preventing such errors from taking place, and of correcting them when formed, is to restrain and simplify our reasoning as much as possible.We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment,
http://web.lemoyne.edu/giunta/EA/LAVPREFann.HTML

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 .

old jim

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davenn
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2021 Award
to induce Current requires there be a closed loop.
to induce EMF does not.

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

refer to your quote in my signature haha

PhiowPhi and jim hardy
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.

Ow I remember from this.

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.
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.

Yes, I realized the cross product between the velocity and the magnetic field.
But can't explain why in terms of the math.

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sophiecentaur