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# Physics/The magnetic field surrounding a current-carrying wire

Question

Current around a wire
Hello Steve,

Thanks for all your help with my previous question. It helped me understand the situation a lot! This has also thrown up new questions I have been thinking on.

I was wondering if I could ask a question on the magnetic field surrounding a current-carrying wire, and how this field might change with the presence of other, ferrous materials nearby.

I have been using this web page
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c3
to calculate the magnetic field around the wire, which the page shows moving in concentric circles.
The site gives the formula B = (μ0*I)/(2*pi*r) Where I is the current in Amperes, and r is the distance from the wire in meters.
This formula is for a wire surrounded by air, but I am wondering what might happen if some other objects were close to the wire (as close as r in the formula)

As you can see in the attached image, I am interested in a situation where a high permeability object and a low permeability object are positioned equal distance from the wire.
Can we assume the presence of the high permeability material would make the magnetic field around the wire stronger?
If the goal was to exert a stronger force on the low permeability object, would the resulting magnetic field have a stronger effect on the low permeability object?
Do you think the field would still flow in a concentric circle, or would the field be diverted in the direction of the high permeability material?

I hope I have explained clearly!

Thanks again and best regards,
Eddie

Hello Eddie,

I think the following web site will help you understand what would happen in the case you describe.
http://mumetal.co.uk/?p=106
Notice Figures 1 and 3 in particular. The presence of a higher permeability substance in a magnetic field distorts the field so that the density of the field in the substance is higher than it would be in that space without the substance. Notice the return of the normal shape of the field away from the substance. Notice in Figure 1 that the 2 topmost field lines have abandoned the area above the high permeability object, preferring instead to flow through the object.

So perhaps you can see why an iron core makes a solenoid stronger. With just an air core, the field can be somewhat unorganized and some of the lines would sort of wander off. But having an iron core, the field happily flows through the core and emerges at the end full strength (or at least more so). (Forgive the unprofessional discussion. Sometimes I visualize better if I think in terms of technical phenomena having some preferences in their behavior.)

I hope this helps,
Steve
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you Steve. Always appreciated!

Physics

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#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University