Solenoid with current carrying wire inside

AI Thread Summary
The discussion revolves around calculating the magnetic field in a solenoid with a current-carrying wire at its center, where the wire has a different permeability than the surrounding medium. The magnetic field equations for different regions are outlined, with specific attention to the effects of varying permeability values. The magnetic field direction from the wire is noted to be in the -a_φ direction, while that from the solenoid is in the z-direction. The impact of the wire's permeability, especially if it is made of a magnetic material like iron, is emphasized, suggesting the use of the equation B=μH for accurate calculations. The problem highlights the need to differentiate between the currents in the solenoid and the wire for a comprehensive understanding of the magnetic fields involved.
meaghan
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Homework Statement


I have a solenoid with a wire carrying current in the center. The wire has a radius of a, the solenoid has a radius of b. I need to find the magnetic field inside of each region. Inside of the wire, mu =/= muo.
upload_2017-10-29_13-28-58.png


Homework Equations


Wire B field = uo I/2*pi*r
Solenoid B field = N/length *I

The Attempt at a Solution



When the r<a:
mu*n*I/length - mu*I*r/(2*pi*a^2)

When a<r<b
mu*n*I/length - mu*I/(2*pi*r

When r> b
then the solenoid will have no magnetic field,
I*mu/2*pi*r

I'm confused how the different mu values would factor into the equation. I'm 90% sure I did this correct
 

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The magnetic field from the current carrying wire down the middle is in the ##- \hat{a}_{\phi} ## direction. Meanwhile, the magnetic field from the solenoid turns is in the ## \hat{z} ## direction.
 
Charles Link said:
The magnetic field from the current carrying wire down the middle is in the ##- \hat{a}_{\phi} ## direction. Meanwhile, the magnetic field from the solenoid turns is in the z-direction.
I forgot my directions. Does the wires having a different value for mu than air affect anything? I solved it first using H and then I got to getting the magnetic field and I was confused how it would affect it.
 
meaghan said:
I forgot my directions. Does the wires having a different value for mu than air affect anything? I solved it first using H and then I got to getting the magnetic field and I was confused how it would affect it.
The wire down the middle could be made of e.g. iron which is a reasonably good conductor, and is also a magnetic material. In this case, the equation ## B=\mu H ## applies, where ## H=B/\mu_o ## is the ## H ## field from the solenoid plus the ## H ## field from the current in its own wire. (Use Biot-Savart and/or Ampere's law to compute it). Note: ## \mu=\mu_o \mu_r ## where ## \mu_r ## is the relative permeability of the (iron) wire. (A value for ## \mu_r \approx 500 ## is quite common for iron). The wire of the solenoid is assumed to be of a non-magnetic material. ## \\ ## Additional item: It may puzzle you how the equation ## B=\mu H ## originates. The magnetic material (for uniform magnetization) has magnetic surface currents that generate a magnetic field (## B_m ##) inside the magnetic material that is equal to ## M ##, so that ## B=\mu_o H+M ## and ## M= \mu_o \chi_m H ##. This makes ## B=\mu H ## with ## \mu=\mu_o (1+\chi_m) ## . For an introduction to this concept, see https://www.physicsforums.com/threads/magnetic-field-of-a-ferromagnetic-cylinder.863066/ You can also just use the formula ## B=\mu H ##, but it is good to have some idea of the origins of this formula. ## \\ ## Additional note: In the above, I've omitted the vector symbol, but I'm really meaning ## \vec{B}=\mu \vec{H} ##, etc. ## \\ ## And additional item: The more common problem is the long solenoid with an iron core. This problem adds the additional detail of running a DC current through that iron core. One thing the problem could specify more clearly is that there are two different currents: that of the solenoid ## I_s ## , and that of the wire ## I_w ## .
 
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