Advanced Electricity and Magnetism Advanced Electricity and Magnetism Physics Help Forum 
Jun 10th 2015, 06:36 AM

#1  Member
Join Date: Jun 2014
Posts: 67
 Ampere's law and magnetic circuit
For magnetic circuit there is an equation NI=HL. This equation is obtained by applying Ampere's law. H is magnetic field intensity and L is the length of the circuit. In following picture the equation reduced to I=HL as there is only one turn: https://www.dropbox.com/s/22rgm63vud...itled.png?dl=0
However, if take a shorter path and apply the Ampere's law, HL must be smaller than before due to shorter path but there is still same current I enclosed (see below). Why? https://www.dropbox.com/s/9mbbi49q38...itled.jpg?dl=0
btw, sorry for the ugly picture.

 
Jun 10th 2015, 10:42 AM

#2  Senior Member
Join Date: Apr 2008 Location: Bedford, England
Posts: 668

I initially left this because I am not really familiar with electromagnetic induction
(I vaguely remember I did it at school, but that was loooong ago).
However, just following the equations you posted,
If the current I is the same, and the loop length L is smaller, then it surely follows that the magnetic field intensity H must be bigger?
Hopefully someone else will jump in if I've made (yet another) mistake...
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Jun 10th 2015, 07:42 PM

#3  Member
Join Date: Jun 2014
Posts: 67

Originally Posted by MBW I initially left this because I am not really familiar with electromagnetic induction
(I vaguely remember I did it at school, but that was loooong ago).
However, just following the equations you posted,
If the current I is the same, and the loop length L is smaller, then it surely follows that the magnetic field intensity H must be bigger?
Hopefully someone else will jump in if I've made (yet another) mistake... 
The problem is how H can be bigger? Just see the pictures and you will know what problem it is.

 
Jun 11th 2015, 03:17 AM

#4  Junior Member
Join Date: Jun 2015 Location: india
Posts: 27

I think you have to think more about the concept behind equation
do you think that considering any shape around the conductor you can find H along the shape just by dividing I with L (by your eqn I=HL).
There you got a mistake
as long as currnt through your shape is constant HL will be constant but dont think about H and L individually .bcoz when you take each point on your shape considered at many of points H will be differnt since your shape is not symmetric and not circular about the conductor(if the shape is symmetric and circular then you can find H along the circle just by doing I/L ).otherwise when you look at H individually your are getting an absolutely meaningfull
number
Last edited by Steve; Jun 11th 2015 at 03:33 AM.

 
Jun 11th 2015, 04:35 AM

#5  Member
Join Date: Jun 2014
Posts: 67

Originally Posted by Steve I think you have to think more about the concept behind equation
do you think that considering any shape around the conductor you can find H along the shape just by dividing I with L (by your eqn I=HL).
There you got a mistake
as long as currnt through your shape is constant HL will be constant but dont think about H and L individually .bcoz when you take each point on your shape considered at many of points H will be differnt since your shape is not symmetric and not circular about the conductor(if the shape is symmetric and circular then you can find H along the circle just by doing I/L ).otherwise when you look at H individually your are getting an absolutely meaningfull
number 
I have considered the point you have mentioned. Actually I have considered this before that leads to this post.
Yes, H is supposed to be different. But in the iron core it is uniform or approximately uniform. Now try to apply Ampere's law. If you do the integration in the path of picture one you get HL where L is length of core. Then do the integration for the second path, you will find that part of it have the same H because it is inside the iron core, but part of it is outside the core so the H is essentially zero. Therefore, the second integration is smaller than the first one. The problem is, Ampere's law says that the integration is always equals to I (only one single turn of electric wire). That is the dilemma.

 
Jun 11th 2015, 10:39 AM

#6  Senior Member
Join Date: Apr 2008 Location: Bedford, England
Posts: 668

I'm not sure you can say the magnetic field is only within the iron core,
The field is certainly influenced and shaped by the core,
You can say it is concentrated within the core,
but I don't think it is correct to say it is zero outside the core.
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Jun 11th 2015, 05:52 PM

#7  Junior Member
Join Date: Jun 2015 Location: india
Posts: 27

Originally Posted by kelsiu I have considered the point you have mentioned. Actually I have considered this before that leads to this post. Yes, H is supposed to be different. But in the iron core it is uniform or approximately uniform. Now try to apply Ampere's law. If you do the integration in the path of picture one you get HL where L is length of core. Then do the integration for the second path, you will find that part of it have the same H because it is inside the iron core, but part of it is outside the core so the H is essentially zero. Therefore, the second integration is smaller than the first one. The problem is, Ampere's law says that the integration is always equals to I (only one single turn of electric wire). That is the dilemma. 
I go with MBW that magnetic feild is not at all zero ouside the core,even though it it is concentrated inside it i dont uderstand how you came to conclude feild is unform inside the core .Around a conductor magnectic feild is uniform at all points which are equally distant from it .points of a square will never be equidistant from it ,if it was a circle with conductor passing right through center then feild will be unform all over it ,since all points are equodostant from it

 
Jun 12th 2015, 06:19 AM

#8  Member
Join Date: Jun 2014
Posts: 67

Originally Posted by Steve I go with MBW that magnetic feild is not at all zero ouside the core,even though it it is concentrated inside it i dont uderstand how you came to conclude feild is unform inside the core .Around a conductor magnectic feild is uniform at all points which are equally distant from it .points of a square will never be equidistant from it ,if it was a circle with conductor passing right through center then feild will be unform all over it ,since all points are equodostant from it 
Maybe I quote from a textbook:
The analysis of a transformer is based on three stated assumptions:
1. The magnetic fluxes of all turns of the coil are linked.
2. The magnetic flux is contained exclusively within the magnetic core.
3. The flux density is uniform across the crosssectional area of the core.
Although they are only assumptions they supposed to be closed to real situation.
Besides you and MBW, there are some people in other forum suggested the same thing: the flux outside is not zero. I have also considered this before I posted the question. However, we may still get a smaller result if the field is close to zero. That's why I asked.

 
Jun 12th 2015, 06:39 PM

#9  Junior Member
Join Date: Jun 2015 Location: india
Posts: 27

Did you heard about Oested's experimnt .He was the man,though accedently,found out a compass needle placed near a conductor having current shows a difflection . If there is no mag. feild outside then how could that happen. Secondly,you have said that mag. field will be smaller than in first case. But you have to consider the distance of point you consider to measure mag.feild . Since mag.feild around a conductor is inversly propotional on distance from it. In the larger rectangle more points are larger distance. Can you please tell weather the quantity H in your equation is medium depended or not.If it is medium depended then your eqn do have 1 correction HL=eNI here e is epsilon. Or else H is medium independent then your eqn is correct and then why do you have to bother about the core and air .in both H will be same at points which equi distant frm conductor
Last edited by Steve; Jun 13th 2015 at 05:50 PM.

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