Understanding Induced Current and EMF in Electromagnetic Induction

[BruceW]

But it becomes indeterminate. What is the value? What is the path of integration? When a conductor is present there is a definite path of integration meaning that we can compute a specific value. Without a conductor where is the path? How can we transport a charge along an arbitrary path without a conductor in place? Think about what you're saying.

If we define emf as the closed integral of E*dL, then you can choose whatever path of integration you want. That's the beauty of Maxwell's equations. An emf does not necessarily have to cause a movement of charge. Of course, you can define emf differently. I don't know what is the most commonly-used definition of emf.

 

[jsmith613]

This is your set up (just as I imagined) but I want to know where these currents you refer to are flowing (as you see it). This must involve you putting some arrows with labels on that diagram. I still can't see how you are thinking with this.

here is a labelled diagram
or a better image:

 

[BruceW]

yes, if we assume the magnet goes down smoothly, then the induced currents will circulate horizontally (which doesn't happen in practise, but it might be a useful approximation). I see where you're coming from now. So what was your question about emf? (And I'll assume we're talking about emf over a horizontal path around the tube)

 

[jsmith613]

yes, if we assume the magnet goes down smoothly, then the induced currents will circulate horizontally (which doesn't happen in practise, but it might be a useful approximation). I see where you're coming from now. So what was your question about emf? (And I'll assume we're talking about emf over a horizontal path around the tube)

well will either of them be zero for the time the magnet is in the tube?

 

[BruceW]

Were you wondering (in this idealised motion), if the currents going anticlockwise below the magnet are equal in magnitude to the clockwise currents above the magnet? I see no reason why not. The magnet produces the same amount of magnetic field on either side, so the magnetic flux change on both sides is the same.

 

[jsmith613]

Were you wondering (in this idealised motion), if the currents going anticlockwise below the magnet are equal in magnitude to the clockwise currents above the magnet? I see no reason why not. The magnet produces the same amount of magnetic field on either side, so the magnetic flux change on both sides is the same.

so you would agree then that the net EMF and current is zero?

 

[BruceW]

well will either of them be zero for the time the magnet is in the tube?

either of what be zero?

 

[BruceW]

so you would agree then that the net EMF and current is zero?

you mean that there is the same amount of current going clockwise as there is anti-clockwise? Again, I see no reason why not.

 

[jsmith613]

either of what be zero?

the current or emf

 

[BruceW]

the current or emf

They won't be zero. But as I said in my last post, I would guess that there is as much current going anti-clockwise as there is current going clockwise. The magnet is dipole, so I see no reason to break symmetry of clockwise and anti-clockwise.

 

[jsmith613]

They won't be zero. But as I said in my last post, I would guess that there is as much current going anti-clockwise as there is current going clockwise. The magnet is dipole, so I see no reason to break symmetry of clockwise and anti-clockwise.

but why won't they be zero
1 + (-1) = 0
??

 

[truesearch]

Phew! I wonder what Faraday would make of that lot!
Your falling magnet in the copper tube...the induced currents flow around the tube but the current at the bottom is induced to repel the S pole, the one at the top is induced to attract the N pole.
Both currents are induced to generate S poles... They are in the same direction.
This is the difference between the tube with a falling magnet and the (thin) coil with a magnet falling through.

 

[BruceW]

but why won't they be zero
1 + (-1) = 0
??

the charges above the magnet need to go clockwise and the charges underneath need to go anticlockwise (to slow the descent of the magnet). So there is not the same amount of charges going in either direction at all points in space.

 

[jsmith613]

Phew! I wonder what Faraday would make of that lot!
Your falling magnet in the copper tube...the induced currents flow around the tube but the current at the bottom is induced to repel the S pole, the one at the top is induced to attract the N pole.
Both currents are induced to generate S poles... They are in the same direction.
This is the difference between the tube with a falling magnet and the (thin) coil with a magnet falling through.

no but when produces a south pole up and the other a south pole down?

 

[jsmith613]

the charges above the magnet need to go clockwise and the charges underneath need to go anticlockwise (to slow the descent of the magnet). So there is not the same amount of charges going in either direction at all points in space.

so is this diagram wrong:
http://www.thestudentroom.co.uk/attachment.php?attachmentid=139647&d=1333538964

I don't want to show the image here as it is enourmous

 

[BruceW]

Phew! I wonder what Faraday would make of that lot!
Your falling magnet in the copper tube...the induced currents flow around the tube but the current at the bottom is induced to repel the S pole, the one at the top is induced to attract the N pole.
Both currents are induced to generate S poles... They are in the same direction.
This is the difference between the tube with a falling magnet and the (thin) coil with a magnet falling through.

I think they are in different directions. Because they are acting to decrease the change in magnetic flux.

 

[truesearch]

A S pole is needed at each end of the magnet to cause opposition to motion

 

[jsmith613]

A S pole is needed at each end of the magnet to cause opposition to motion

look at the diagram on the previous page
it shows why currents are in different directions

 

[BruceW]

so is this diagram wrong:
http://www.thestudentroom.co.uk/attachment.php?attachmentid=139647&d=1333538964

I don't want to show the image here as it is enourmous

That is a different situation, it is measuring the emf along the entire coil.

 

[jsmith613]

That is a different situation, it is measuring the emf along the entire coil.

so if I were to measure the emf across the entire tube (with the magnet falling) - assuming it were possible - would the current and emf be measured as zero?

 

[truesearch]

Gnight for now

 

[BruceW]

so if I were to measure the emf across the entire tube (with the magnet falling) - assuming it were possible - would the current and emf be measured as zero?

I'm pretty sure emf between the top and bottom of the tube would be zero. In the case of the coil, an emf is measured when the magnet falls into it because the measured emf is effectively the total emf over the horizontal loops, so it will be non-zero when the magnet falls in (and out). But with the tube, you would be measuring the potential difference between the top of the tube and bottom, which will be zero. Its only if you had some other technology, or way of seeing the charge carriers that you would realize something is going on in the case of the tube.

 

[sophiecentaur]

so you would agree then that the net EMF and current is zero?

You still need to define what you mean by "NET".
The only time I would use that term would be in a situation where, for example, forces on a point would Add Up to a 'net' or 'resultant value'. But these currents are all over the place so I think you must mean 'Mean Value' but Mean Value over what? Just the peak values? It is not as simple as you imply, I think. Decide what you really mean and we can come up with an answer.

 

[jsmith613]

I'm pretty sure emf between the top and bottom of the tube would be zero. In the case of the coil, an emf is measured when the magnet falls into it because the measured emf is effectively the total emf over the horizontal loops, so it will be non-zero when the magnet falls in (and out). But with the tube, you would be measuring the potential difference between the top of the tube and bottom, which will be zero. Its only if you had some other technology, or way of seeing the charge carriers that you would realize something is going on in the case of the tube.

just to absolutely clarify and then I think I have gotten it, the current too will be measured as zero between the ends of BOTH the coil and the tube, right?

 

[jsmith613]

You still need to define what you mean by "NET".
The only time I would use that term would be in a situation where, for example, forces on a point would Add Up to a 'net' or 'resultant value'. But these currents are all over the place so I think you must mean 'Mean Value' but Mean Value over what? Just the peak values? It is not as simple as you imply, I think. Decide what you really mean and we can come up with an answer.

well I mean the EMF/current across the ends of the tube / coil
I think maybe the word net / mean was a poor way of saying this

 

[sophiecentaur]

That diagram of the coil would suggest otherwise, wouldn't it?

 

[jsmith613]

That diagram of the coil would suggest otherwise, wouldn't it?

sorry the diagram of the coil suggests exactly this...

 

[jsmith613]

I am off for tonight
we can carry on tomorrow
I continue to express my graditude for all the help you have been giving me (in fact if this is the first time I have said it I really do emphasise how grateful I am for all your help so far :)

 

[BruceW]

just to absolutely clarify and then I think I have gotten it, the current too will be measured as zero between the ends of BOTH the coil and the tube, right?

For the case of the coil, when the magnet is falling into (or out of) the coil, there will be a flow of charge through the coil, to slow the rate of change of flux. But when the magnet is in the middle of the coil, the charges above the magnet want to go clockwise and those underneath the magnet want to go anticlockwise. But this would cause a charge separation, so when the magnet is in the middle, there is no flow of charge.

For the case of the tube, in reality there are lots of eddy currents that try to slow the rate of change of flux caused by the tumbling magnet. If the magnet went down smoothly as you've suggested, it seems plausible that there would be charges flowing anti-clockwise underneath the magnet and clockwise above the magnet (really they are just very ordered eddy currents). These eddy currents continue even as the magnet is falling through the middle of the tube.

In the coil, it is simple to measure the emf which causes the circular flow of charge, because of the fact that it is set-up as a coil. But in the tube, I can't think of a simple way of measuring the flow of charges, and if you just measured the emf between the top and bottom of the tube, I'm pretty sure you'd get nothing, or in any case it would not tell you about the circular flow of charge which is acting to decrease the magnet's acceleration.

I continue to express my graditude for all the help you have been giving me (in fact if this is the first time I have said it I really do emphasise how grateful I am for all your help so far :)

Ah, I'm glad if I've even been of some help.

Edit: maybe you were just saying this to sophiecentaur... I am so quick to accept a thank you

 

[sophiecentaur]

sorry the diagram of the coil suggests exactly this...

The diagram has an oscilloscope trace in it which shows that the EMF is not Zero at all times. How can the following statement be right? Earlier you wrote this:

just to absolutely clarify and then I think I have gotten it, the current too will be measured as zero between the ends of BOTH the coil and the tube, right?

When is it measured as zero? You seem to have a problem with using the term 'Mean'. This is a bit of a handicap in discussions in which both time and position vary. Your term 'Net' doesn't make it clear what you want to say.

I am sorry but I have just followed an endless and frustrating thread, elsewhere, in which one of the contributors absolutely refused to use the right terms appropriately - mixing up force, strength, power etc. in a totally random way. The thread ended without his getting anywhere. I am very sensitive to this sort of thing at the moment, which is why I think the right terminology is important. Unless we agree on the terms to use and what they mean then we may not get anywhere either.
I am assuming you are familiar with the term?

 

[jsmith613]

I am assuming you are familiar with the term?

what term??

 

[jsmith613]

Edit: maybe you were just saying this to sophiecentaur... I am so quick to accept a thank you

absolutely this was aimed at you and everyone else who has helped me!

 

[jsmith613]

The diagram has an oscilloscope trace in it which shows that the EMF is not Zero at all times. How can the following statement be right? Earlier you wrote this:

Oh I see
the question I was asking was for the entire time the magnet is INSIDE THE TUBE
obviously as it approaches / leaves there will be a change in flux BUT INSIDE THE TUBE the emf on the oscilliscope is zero.
look. the magnet is dropped from ABOVE THE COIL so obviously as it falls the emf will increase but my question was is it correct to assume that WHEN THE EMF IS ZERO, the current will also be zero

When I said MEAN/NET I meant WHILST THE MAGNET WAS IN THE TUBE

 

[sophiecentaur]

Right. Whilst inside the coil there is no induced EMF so the meter reads zero. This IS (and I see what you mean here) the NET instantaneous effect of the passage of the N and S poles along the coil length. They are only unbalanced when one pole is inside and one pole is outside the coil (at the ends).

Whilst the magnet is falling inside the tube there are EMFs being produced at all times which are producing circulating currents. Without the currents, the magnet wouldn't be slowed up, would it? These EMFs (and hence the currents) are in 'Lenz's Law' directions. BUT the Mean of all the EMFs around the magnet will be zero because both ends of the magnet are traveling at the same speed.

There is no reason to think that an EMF would ever be measured over the length of the tube because the axis of the tube (the conductor) is not at right angles to the direction of the motion. EMFs are induced around the circumference.

@Bruce You mention the problem of measuring the currents inside the tube. It would be possible to cut the tube, horizontally, half way down and insert an insulated split ring. You could measure the EMF across the gap in the ring and then this could 'indicate' the value of current, knowing the resistivity of the tube metal. The magnet would need to be not tumbling, of course.

 

[jsmith613]

Right. Whilst inside the coil there is no induced EMF so the meter reads zero. This IS (and I see what you mean here) the NET instantaneous effect of the passage of the N and S poles along the coil length. They are only unbalanced when one pole is inside and one pole is outside the coil (at the ends).

Whilst the magnet is falling inside the tube there are EMFs being produced at all times which are producing circulating currents. Without the currents, the magnet wouldn't be slowed up, would it? These EMFs (and hence the currents) are in 'Lenz's Law' directions. BUT the Mean of all the EMFs around the magnet will be zero because both ends of the magnet are traveling at the same speed.

Ok so I think you are saying that the mean emf will be zero but the mean current WILL NOT BE otherwise the magnetic field would not be produced, right?