Analyzing Magnetic Field of an Infinite Cylinder with Constant Magnetization

In summary, if an infinite slab between z=0 and z=d (thickness d) is uniformly magnetized in the x direction, then the electric field is -2πρd\hat{z}
  • #36
According to what you just posted, should I then simply substitute the appropriate j (in terms of M and c) for each of the two planes with fields 2*pi*j/c?
 
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  • #37
peripatein said:
According to what you just posted, should I then simply substitute the appropriate j (in terms of M and c) for each of the two planes with fields 2*pi*j/c?

Yes :smile:
 
  • #38
But won't they cancel out each other (I mean, upon summation of both contributions)? That is, won't the net magnetic field within the slab be zero?
 
  • #39
Are the currents in the two surfaces in the same direction or opposite direction?
 
  • #40
Based on j, opposite.
 
  • #41
Yes, so will the two fields inside the slab from the two currents be in the same direction or opposite direction?
 
  • #42
Using the RHR the fields would form a unified field of 4*p*M is the positive z direction. Do you agree?
 
  • #43
peripatein said:
Using the RHR the fields would form a unified field of 4*p*M is the positive z direction. Do you agree?

Yes, if you meant to say in the positive x direction.
 
  • #44
Why not z?
 
  • #45
Think about it. (Got to go eat dinner now!)
 
  • #46
Hmm... I find it a bit strange, as curling my fingers around a current conducting wire in the y direction, I seem to be getting a magnetic field in the z direction (coming out of the sheet to the left of the wire and entering the sheet to its right)!
 
  • #47
Consider the upper current sheet with current in the negative y direction, as shown. Suppose you want B at point P. Take two symmetrically placed current elements (shown in red). What would be the direction of the net B at P from these two current elements?
 

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  • #48
I do see it, using B-S Law and the RHR, but why didn't my initial application of the RHR get me there? Why did the RHR "seemingly" yielded the wrong result? Also, how could I have convinced myself that there was no volumetric charge density rho and only surface density? Is it because based on Gauss's Law a volumetric charge density would entail an electric field and there is none in this set-up?
 
  • #49
peripatein said:
I do see it, using B-S Law and the RHR, but why didn't my initial application of the RHR get me there? Why did the RHR "seemingly" yielded the wrong result?
I believe it was because you were considering the field of only one straight wire of current rather than the superposition of the fields of all the current elements in the surface.

Also, how could I have convinced myself that there was no volumetric charge density rho and only surface density? Is it because based on Gauss's Law a volumetric charge density would entail an electric field and there is none in this set-up?

ρ would result from a nonuniform electric polarization P. But here we have only magnetic polarization M.
 
  • #50
Could we have combined both M in the x direction (this set up) and P in the z direction (previous set up) into a new set up? Will it make any sense?
 
  • #51
peripatein said:
Could we have combined both M in the x direction (this set up) and P in the z direction (previous set up) into a new set up? Will it make any sense?

In principle I think you could have both P and M. I don't see why not.
 
  • #52
Thank you so, so much, TSny! You were incredibly kind and helpful :-).
 
<h2>1. What is the purpose of analyzing the magnetic field of an infinite cylinder with constant magnetization?</h2><p>The purpose of this analysis is to understand the behavior of the magnetic field surrounding an infinitely long cylinder with a constant magnetic field. This can provide insights into the properties and interactions of magnetic materials, as well as aid in the design of devices that utilize magnetic fields.</p><h2>2. How is the magnetic field of an infinite cylinder with constant magnetization calculated?</h2><p>The magnetic field of an infinite cylinder with constant magnetization can be calculated using the Biot-Savart law, which relates the magnetic field at a point to the current flowing through a wire. In this case, the wire is replaced by an infinitely long cylinder with a constant magnetization.</p><h2>3. What factors affect the magnetic field of an infinite cylinder with constant magnetization?</h2><p>The strength of the magnetic field of an infinite cylinder with constant magnetization is affected by the magnitude and direction of the magnetization, as well as the distance from the cylinder. Additionally, the magnetic properties of the surrounding medium can also have an impact on the field.</p><h2>4. Can the magnetic field of an infinite cylinder with constant magnetization be visualized?</h2><p>Yes, the magnetic field of an infinite cylinder with constant magnetization can be visualized using magnetic field lines. These lines represent the direction and strength of the magnetic field at different points surrounding the cylinder.</p><h2>5. How is the magnetic field of an infinite cylinder with constant magnetization used in practical applications?</h2><p>The magnetic field of an infinite cylinder with constant magnetization has various practical applications, such as in magnetic storage devices, MRI machines, and magnetic levitation systems. It can also be used in the development of new materials and technologies that utilize magnetic fields.</p>

1. What is the purpose of analyzing the magnetic field of an infinite cylinder with constant magnetization?

The purpose of this analysis is to understand the behavior of the magnetic field surrounding an infinitely long cylinder with a constant magnetic field. This can provide insights into the properties and interactions of magnetic materials, as well as aid in the design of devices that utilize magnetic fields.

2. How is the magnetic field of an infinite cylinder with constant magnetization calculated?

The magnetic field of an infinite cylinder with constant magnetization can be calculated using the Biot-Savart law, which relates the magnetic field at a point to the current flowing through a wire. In this case, the wire is replaced by an infinitely long cylinder with a constant magnetization.

3. What factors affect the magnetic field of an infinite cylinder with constant magnetization?

The strength of the magnetic field of an infinite cylinder with constant magnetization is affected by the magnitude and direction of the magnetization, as well as the distance from the cylinder. Additionally, the magnetic properties of the surrounding medium can also have an impact on the field.

4. Can the magnetic field of an infinite cylinder with constant magnetization be visualized?

Yes, the magnetic field of an infinite cylinder with constant magnetization can be visualized using magnetic field lines. These lines represent the direction and strength of the magnetic field at different points surrounding the cylinder.

5. How is the magnetic field of an infinite cylinder with constant magnetization used in practical applications?

The magnetic field of an infinite cylinder with constant magnetization has various practical applications, such as in magnetic storage devices, MRI machines, and magnetic levitation systems. It can also be used in the development of new materials and technologies that utilize magnetic fields.

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