Magnetic Field And Current

Thread Starter

DD Ki Vines

Joined Apr 20, 2019
21
I have a question for a long time

We all know that integrating Electric field over a distance or over a line gives the work done by Electric field which is voltage

Similarly we know integrating Magnetic field over a closed loop gives us the current my question is why? Why integrating magnetic field over a closed loop gives current? And what physical significance the integration itself has?
like integrating Electric field over a distance gives the work done by the electric field what does integrating magnetic field over a closed loop give?

Please don't give this answer: current create magnetic field so integrating magnetic field gives current,I know that
 

Papabravo

Joined Feb 24, 2006
21,159
It may help to look at the units of the integrand and the result. For example, if you integrate a constant acceleration with respect to time, you get a constant times seconds(a unit of time). What can you conclude from this?
 

Thread Starter

DD Ki Vines

Joined Apr 20, 2019
21
It may help to look at the units of the integrand and the result. For example, if you integrate a constant acceleration with respect to time, you get a constant times seconds(a unit of time). What can you conclude from this?
Sir actually I can't conclude anything from this because the unit of magnetic field strength (H) which is A/m is derived from the mathematical expression "integrating H field over a closed loop gives current" itself. I just need answer to a simple question why integrating magnetic field gives current and what physical significance does the integration itself has
 

Papabravo

Joined Feb 24, 2006
21,159
You integrate the B field over the loop. B has units of Tesla. The constant μ₀ has units of N/A²
You asked what happens when you integrate, and I told you, but you have to integrate the right thing.
 

MrAl

Joined Jun 17, 2014
11,389
I have a question for a long time

We all know that integrating Electric field over a distance or over a line gives the work done by Electric field which is voltage

Similarly we know integrating Magnetic field over a closed loop gives us the current my question is why? Why integrating magnetic field over a closed loop gives current? And what physical significance the integration itself has?
like integrating Electric field over a distance gives the work done by the electric field what does integrating magnetic field over a closed loop give?

Please don't give this answer: current create magnetic field so integrating magnetic field gives current,I know that

This might give you a better feel for it intuitively...

Do you know what a "lead screw" is? (pronounced "leed" screw)
Just in case you dont, it is a screw that is usually turned and it causes some piece it is threaded into to move in a linear fashion. But the converse is also true: if you turn the piece it is threaded into and hold it stationary, you can get the lead screw to move in and out depending on the direction of rotation. So in this case, you turn the piece and the lead screw moves left, then you turn the piece the other way and the lead screw moves right. If you had a really, really, long lead screw (several meters or even several miles) you could get that lead screw to move for a very very long time, and if that lead screw was a very very large circular lead screw that bent around gently and both ends connected together, when you turned the piece it was threaded into the lead screw would turn indefinitely as long as you turned the piece continuously.

If you can understand that, congratulations, now you understand the mechanism behind the magnetic field and the current in the wire, because the magnetic field acts as the piece turning continuously and the circular lead screw acts as the current.
If you count the threads of the lead screw as it passes a fixed point, you would count a fixed number N if the piece was turned at a constant rate, and if you increase the speed of the piece turning, the number N would go up. That's how the current and magnetic field are related to each other. As the field increases, the current increases.

This is quite eloquently described by one of Maxwells equations:
curl B=J*u0

and what you observed in the demonstration above with the lead screw is the curl. For that kind of movement in 3d the result is a movement in only one dimension and that is the direction of the current (looking at a small section of the lead screw or wire).

Another way of looking at it is that the piece has a 'crank' handle on it and you continuously turn the piece using the crank handle and the lead screw moves accordingly.

Does that help :)
 

Thread Starter

DD Ki Vines

Joined Apr 20, 2019
21
This might give you a better feel for it intuitively...

Do you know what a "lead screw" is? (pronounced "leed" screw)
Just in case you dont, it is a screw that is usually turned and it causes some piece it is threaded into to move in a linear fashion. But the converse is also true: if you turn the piece it is threaded into and hold it stationary, you can get the lead screw to move in and out depending on the direction of rotation. So in this case, you turn the piece and the lead screw moves left, then you turn the piece the other way and the lead screw moves right. If you had a really, really, long lead screw (several meters or even several miles) you could get that lead screw to move for a very very long time, and if that lead screw was a very very large circular lead screw that bent around gently and both ends connected together, when you turned the piece it was threaded into the lead screw would turn indefinitely as long as you turned the piece continuously.

If you can understand that, congratulations, now you understand the mechanism behind the magnetic field and the current in the wire, because the magnetic field acts as the piece turning continuously and the circular lead screw acts as the current.
If you count the threads of the lead screw as it passes a fixed point, you would count a fixed number N if the piece was turned at a constant rate, and if you increase the speed of the piece turning, the number N would go up. That's how the current and magnetic field are related to each other. As the field increases, the current increases.

This is quite eloquently described by one of Maxwells equations:
curl B=J*u0

and what you observed in the demonstration above with the lead screw is the curl. For that kind of movement in 3d the result is a movement in only one dimension and that is the direction of the current (looking at a small section of the lead screw or wire).

Another way of looking at it is that the piece has a 'crank' handle on it and you continuously turn the piece using the crank handle and the lead screw moves accordingly.

Does that help :)
Sir ur explanation is indeed very good but unfortunately it's not the answer to my question what ur telling me is how magnetic field and current works,the mechanism behind it but my question is why magnetic field and current work in that way? I know current creates magnetic field that's natural law but I want to know why integrating magnetic field gives current? And specifically I want to know,like integrating Electric field over a distance or a line gives work done by the field or voltage,what, integrating magnetic field over a closed loop,gives?
 

Papabravo

Joined Feb 24, 2006
21,159
Once again. the process of integration does things to the order of the quantities in the integrand. For polynomials it raises the order of each term of the independent variable. It must do the same thing for every function that can be represented by a series expansion. Mathematically, it could not be otherwise. You integrate B dot dl and you get current in Amperes along with a constant of proportionality that has units of its own. This presumes the geometry of the strategically chosen loop will cooperate. You can continue to be obstinate, but that has not succeeded in getting you anywhere.
 

Thread Starter

DD Ki Vines

Joined Apr 20, 2019
21
Once again. the process of integration does things to the order of the quantities in the integrand. For polynomials it raises the order of each term of the independent variable. It must do the same thing for every function that can be represented by a series expansion. Mathematically, it could not be otherwise. You integrate B dot dl and you get current in Amperes along with a constant of proportionality that has units of its own. This presumes the geometry of the strategically chosen loop will cooperate. You can continue to be obstinate, but that has not succeeded in getting you anywhere.
Please stop replying vague answers either explain it properly or just admit you don't know the answer and I am not being obstinate I know what I am asking the thing is that all of us has taken this as a defination that integrating magnetic field gives current and that has lead us to success and as we have succeeded no one have questioned why this happen that's the problem I have searched the whole internet,searched several books,asked many teachers in my college no one has ever been able to answer my question correctly and that's why I came here,so if u don't know the answer please stop replying and I know how integration works
 

WBahn

Joined Mar 31, 2012
29,979
You might want to dig out a decent Physics II text and read it very carefully (you are probably in a better position to do that now than when you first went through the material). and focus on what a magnetic field is (in a Physics II sense) and how it relates to all of these quantities.

But the gist of the answer to your question is that when you integrate the magnetic field around a closed path, any current elements that contribute to that magnetic field that lie outside that closed path will cancel out because on some portions they are creating a magnetic field in one direction while in others they are creating a magnetic field in the other. Portions of the path that are nearer to the generating current have a stronger field but over a shorter distance while portions that are further away have a weaker field but over a longer distance. Both effects scale the same with distance, so mathematically they cancel out. The only thing that survives the integral are generating currents like pass through the surface bounded by the path because they are the only ones that can produce a net non-zero result when integrated over the entire path.
 

sparky 1

Joined Nov 3, 2018
756
The explanations took many books. The nomenclature took many years. Hundreds of terms were needed.
Most of which are missing from the one sentence question being asked. So and so said this I don,t understand their point.
Do you mean Faraday, Ampere, Heaviside, Stokes ...
 

MrAl

Joined Jun 17, 2014
11,389
Sir ur explanation is indeed very good but unfortunately it's not the answer to my question what ur telling me is how magnetic field and current works,the mechanism behind it but my question is why magnetic field and current work in that way? I know current creates magnetic field that's natural law but I want to know why integrating magnetic field gives current? And specifically I want to know,like integrating Electric field over a distance or a line gives work done by the field or voltage,what, integrating magnetic field over a closed loop,gives?
Hello again,

Well once you understand the mechanics of it you can go on to figure out why integration or summation gives you the entire picture.

Referring back to my explanation in post #5, the "piece" that the threaded rod threads into is just one of many pieces. Let's imagine that each piece is circular, a disk with a hole in the very center with threads in it where the threaded rod threads into. As you turn the disk, the rod moves left (analogy to current flow). If you apply a certain amount of torque to the disk, the rod (with some friction) the rod moves at a certain speed as the rod itself rotates around its own loop.
Now add a second disk, turning that one along with the first one with the same torque. Now the threaded rod moves faster. Now add more disks, the rod moves even faster yet.
Now let the width of each disk get very small, so that the disks get very narrow but still have their circular shape, then stack them side by side. What is the speed of the rod? The speed is the number of disks times the speed caused by just one disk with the given torque. So if we had five disks, d1, d2, d3, d4, d5, and the speed of one disk was s1, then the total speed would be:
sT=s1+s2+s3+s4+s5
or in summation form:
Total Speed=sum of all s over the length of all the disks together
and if the disks span the entire length of the wire, we get:
Total Speed=sum of all s over the length of the rod.
and each speed s is due to one disk which is dL in width, so we can say that we are summing over the length for each increment in length.

We can observe from that analogy that each narrow disk contributes to the total movement and the sum of all those forces creates the total speed in the same way that the sum of all narrow field segments creates the final current in the wire.
Recall that current i is the rate of change of charge, and the movement of the threaded rod is the rate of change of the rod itself, or taking a microscopic view, the rate of change of each thread of the rod.

Now if you want to know how each dL segment causes the rod or charge to move, you will have to look into how a magnetic field causes charge to move.
 
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