# Induction of Electricity / Faradays Law

Discussion in 'Physics' started by norstudent, Feb 28, 2014.

1. ### norstudent Thread Starter New Member

Feb 26, 2014
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Hi

I'm trying to understand the working principle of an AC motor

Basically the only equation I know in magnetism so far is the equation for the Lorentz force which I know as Fb=q*vxB

Looking at an AC generator, my intuition tells me that we should use this equation for the Lorentz force, for a single particle to find the direction and determine the force, then from there perhaps intergrate over the entire wire to find the total current induced

I see in books/videos however that this seems to be governed by Faradays Law which wikipedia states as:
The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.

Does this mean that the basic equation I know: Fb=q*vxB is somehow realted to (or derived from) Faradays law? What is the relation between them? Can Faradays Law be seen as an extension of the equation for the lorentz force?

2. ### studiot AAC Fanatic!

Nov 9, 2007
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Careful.

The Lorenz force is a mechanical force, applied to a mechanical object.

Faradays law gives the EMF, which is a voltage, generated in a circuit.

3. ### norstudent Thread Starter New Member

Feb 26, 2014
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Ah yes I see

Would it be correct to say that on the particle-level, the EMF is produced due to the lorentz force acting on electrons. The lorentz force thus describes the mechanical force on the particles

And the EMF that we get, which is a voltage, is obtained using Faradays Law?

4. ### studiot AAC Fanatic!

Nov 9, 2007
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I note you have used a simplified version of the Lorenz force equation and that you have used vector form.

The Lorenz force equation combines the effect of electric and magnetic fields on a charge or system (or stream) of charges. The full equation is

${\bf{F}} = e{\bf{E}} + e\left( {{\bf{V}}x{\bf{B}}} \right)$

Where I have used bold caps for vectors.

Yes you can use this for sub atomic charges and equate the force to mass times an acceleration, but in some cases the mass used has to be adjusted and we use something called the 'effective mass', which may be negative in some cases. It gets very complicated, and vector calculus is needed for all but the simplest cases.

So I would not recommend going this route for practical understanding of electrical technology.

Faraday's Law can also be put into vector calculus format but refers to directly to a path in space (ie usefully an electric circuit) so it will yield directly the emf generated by a wire subject to a changing magnetic field.

5. ### norstudent Thread Starter New Member

Feb 26, 2014
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I see! Thanks for the insight!

I'm currently learning the Faraday-lenz Law, but there's one thing im not understanding

The teacher uses an example where we have a magnetic field B coming out of the board. Then we have a wire in a circle somewhere in that magnetic field perpendicular to it, coming out of the page

He then says that if we increase the magnetic field, we increase the flux. Now the system wants to oppose this change, therefore a current is induced where this current will have a magnetic field trying to oppose this change in magnetic flux.

From there on, it's fairly simple to figure out the direction of the current, fingers where the magnetic field needs to point, thumb gives direction of the current

But where does the magnetic field need to point?

We know that the magnetic field, will point in one direction INSIDE the loop, but in a different direction OUTSIDE the loop

So where does it want to oppose the magnetic field (inside or outside this wire loop?) and why?

From one of the examples it seems to me that we have flux only INSIDE this wire loop, is this the case? If so then it makes sense, but WHY do we only have flux inside the loop? The teacher in one example takes B*A and uses the area for this wire loop, 2pi*r, but why? It's just a piece of wire in a cricle, we got air inside it, and air outside it too, right?

6. ### studiot AAC Fanatic!

Nov 9, 2007
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Sorry I'm not following this.

Why does the external field you are going to vary change direction on entering the loop?

Surely its direction is set by whatever is generating it?

7. ### norstudent Thread Starter New Member

Feb 26, 2014
26
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Sorry, let me try to rephrase and be a bit more clear

- You have a straight wire with a current I1 somewhere, current going towards the right
- It sets up the magnetic field B1: magnetic field lines coming out of the paper towards us below it, and going into the paper above it
- In a small distance below it- you place a wire that is in a circle, a loop
- You increase the value B of the magnetic field B1

My objective:
- Calculate the direction of the current in this loop

The approach shown to me:
- Seeing as the flux around this loop is changing: a current will be induced to try oppose this change
- A current will be induced that has a magnetic field of it own in a direction such that it opposes the change in the magnetic flux of the field B

This is where I am unable to tell the direction of the induced current
They are saying the direction of this current must be such that its field opposes the change in the original field B
How can you determine this direction- because the magnetic field from the induced current will both go out of the paper (on the inside of the circle/loop) and out of the paper (on the outside) or visa versa, ie it will go in both directions?

I hope thats clearer, if not then let me know so that I can upload an illustration of what I mean

8. ### norstudent Thread Starter New Member

Feb 26, 2014
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I guess you could also say I'm trying to figure out:
If we have a wire loop with a radius r in a magnetic field B
- How do we calculate the magnetic flux?
- Is it B*Area of circle ie B*2pi*r?

If so: then why do we take the area that is INSIDE the loop, it is just air? Shouldnt we take the circumreference multiply by the thickness of the wire to get the area that is hit by the magnetic field?

9. ### studiot AAC Fanatic!

Nov 9, 2007
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No, sorry.

It is only the flux which threads the loop that generates the EMF, when its flux density changes. That is where the area comes into the reckoning. The greater the area the greater the flux threading the loop at any given density.
If we can clear this up we can move on to the issue of direction. You are quite right in your earlier post to note a possible ambiguity in direction since your search loop has two sides facing opposite ways.

The flux generated by the wire is solenoidal - that is it forms closed loops around the wire at right angles to it.

So it will depend upon the orientation of the loop as to whether the flux generated by the wire threads the search loop or not.

Draw a diagram.

Last edited: Mar 1, 2014
10. ### norstudent Thread Starter New Member

Feb 26, 2014
26
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Yess! This is where my confusion is

Why is it the change in the flux that threads the loop that generate the EMF?
There is nothing inside the loop right it's just air?

And flux is area times B, shouldnt it be the area of the wire (ie the circumreference time the thickness of the wire) and not the area of the hole inside the wire?

Edit:
Ahhh, I also found this:
When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.

I think I understand now, previously I was thinking that the induced magnetic in the wire must oppose the change in the magnetic flux inside the loop & outside the loop! Do you understand my confusion now?

Second edit:
I just reread your statement: "It is only the flux which threads the loop that generates the EMF"
And that clears up my confusion even more!
Why is it like this though? Is there a simple explanation or is it something I should just accepted at something having been proven and a fact of nature?

Last edited: Mar 1, 2014
11. ### norstudent Thread Starter New Member

Feb 26, 2014
26
0
I think I got to the bottom of my confusion. The way I was explained it was that whenever there is a change in magnetic flux, the system does not like this, so it will induce a current in the wire that has a magnetic field that opposes the change in the flux. That is why I was confused, I was thinking that there must be a current induced in the wire that opposes the change in magnetic flux inside the loop and outside the loop as well

But what I found on wikipedia:
The most widespread version of Faraday's law states:
The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.

I think this has corrected my understanding:

Basically Faraday proved that if you have a wire in a closed loop, the enduced EMF is equal to the negative (Actually Lenz proved that negative part, right?) of the time rateof change of the magnetic field THROUGH the circle ie through the circular area inside the wire?

12. ### studiot AAC Fanatic!

Nov 9, 2007
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515
Take a step back and revise the difference between voltage and current.

It is easy to have a voltage without a current.
All you require is for there to be no path for the current to flow as in a disconnected battery.

It is difficult (but not impossible) to have a current without a voltage, most currents are the result of a voltage.
An example on a non volt driven current is a thermionic current.

Now any conductor in a changing magnetic field experiences an EMF generated within it.

This changing magnetic field can be as a result of the conductor and or the field moving or it can be as a result of the field strength changing whilst everything remains still.

We measure the field strength in one of two ways.
As a vector B, the flux density. B is measured in Tesla or webers per square metre.
The total flux $\Phi$ is measured in webers and is product of the flux
density and the area over which it acts.

$\Phi$ = BA

I will return to this equation in the next post.

It really is a good idea to get the units right from the beginning. We have another thread going at the moment (in this subject) where the OP is in all sorts of difficulties because he is not doing this. This problem is very common.

The other way to measure field strength is to use a quantity for which we can draw contours, which we call 'lines of flux'.
This is called the field strength, H, and is measured in Henries. Because the Henry is measured in terms of a standard force produced magnetically by a standard current the Henries corresponds to 1amp per metre., but do not worry about this.

Now to return to what I said at the beginning,

If you have a piece of straight wire and change the magnetic field it encounters, there is no connection between the ends so no current can flow, but an EMF is magnetically induced in it.
This EMF obeys Lenz Law , which is also Faraday's first law.

If you now connect the ends with another conductor, you have a circuit or loop.
Current can now flow, due to this EMF.
This obeys Faraday's second law.

That is why, if we want a current we need an area.

We can discuss the role played by the area in the next installment.

13. ### norstudent Thread Starter New Member

Feb 26, 2014
26
0
Thanks for the response!

Sorry didn't see it until now

The past days ive been going through all the videos on faradays & lenz's law on http://aklectures.com/ which basically cleared it up, but your explanation made it even a bit clearer!