Why can't I use this equation for the magnetic field?

In summary, the net magnetic field at any point inside or outside a material is affected by both the free current and the bound current, with the bound current being dependent on the magnetization of the material. This can result in different equations being used to calculate the magnetic field inside and outside the material, as in the case of using the magnetic susceptibility in the equation for the field inside and not outside. Additionally, bound currents can be created by the alignment of microscopic bound currents in the material, which can contribute to the overall magnetic field.
  • #1
1v1Dota2RightMeow
76
7

Homework Statement



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Homework Equations


##\oint \vec{H} \cdot d\vec{l} = I_{free,enclosed}##
##\vec{B} = \mu_0 (1+\chi _m)\vec{H}##

The Attempt at a Solution


I found the magnetic field inside to be ##\vec{B} = \mu_0 (1+\chi _m)\frac{Is}{2 \pi a^2} \phi##. But why can't I use the same equation (##\vec{B} = \mu_0 (1+\chi _m)\vec{H}##) to solve for the field outside? The answer for the field outside is given as ##\vec{B} = \frac{\mu_0 I}{2 \pi s}##.
 
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  • #2
1v1Dota2RightMeow said:
But why can't I use the same equation (##\vec{B} = \mu_0 (1+\chi _m)\vec{H}##) to solve for the field outside?
You can, but what is the value of ##\chi_m## for points outside the material?
 
  • #3
TSny said:
You can, but what is the value of ##\chi_m## for points outside the material?

Lol yea I took the time to write the question, latex it up, and post, then realized a minute later the answer to my own question...

For further learning: the fact that we have to take into account the magnetic susceptibility of a material leads me to think that the material itself is either strengthening or weakening the magnetic field created by a free current passing through the material. So where do bound currents come into play?
 
  • #4
1v1Dota2RightMeow said:
For further learning: the fact that we have to take into account the magnetic susceptibility of a material leads me to think that the material itself is either strengthening or weakening the magnetic field created by a free current passing through the material.
Yes, that's right. The field of the free current affects the magnetization M of the material which, in turn, affects the net magnetic field. In your example, the magnetization of the material affects only the net field inside the material. The net field outside the wire is due to the free current only. This is not typical. Usually, the magnetization of the material will affect the B field outside the material as well as inside. An extreme example is a magnetized piece of iron which has no free current but still produces plenty of B field outside the material.

So where do bound currents come into play?
There are microscopic (atomic) bound currents that can orient themselves to give a nonzero, effective macroscopic bound current density Jm. https://en.wikipedia.org/wiki/Magnetization#Magnetization_in_Maxwell.27s_equations.
The net magnetic field at any point inside or outside the material is the sum of the fields of the free and bound currents.
 

FAQ: Why can't I use this equation for the magnetic field?

1. Why can't I use this equation for the magnetic field if it worked for a similar experiment?

The magnetic field is dependent on various factors such as the strength of the current, the distance from the source, and the orientation of the magnetic field. Each experiment may have different values for these factors, which can affect the accuracy of the equation in predicting the magnetic field.

2. Can't I just use a simpler equation to calculate the magnetic field?

While simpler equations may exist, they may not take into account all the factors that affect the magnetic field. Using a more complex equation may result in a more accurate calculation.

3. Why do I need to use multiple equations to calculate the magnetic field?

The magnetic field is a vector quantity, meaning it has both magnitude and direction. Therefore, multiple equations are needed to calculate both the magnitude and direction of the magnetic field at a specific point.

4. Can I use this equation for any magnetic field experiment?

No, the equation used for calculating the magnetic field may vary depending on the type of experiment and the setup of the equipment. It is important to use the correct equation for each specific experiment.

5. Why is it important to use the correct equation for the magnetic field?

Using the correct equation ensures that the calculated magnetic field is as accurate as possible. This is important for making precise measurements and for the success of the experiment.

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