Calculating Magnetic Field Strength

Hi All -

Looking for some theory help. I am doing some writing for work showing why resistive heating elements bend and warp due to magnetic fields. The material - MoSi2 - is used for heating applications up to 1900C. I was talking to one of the Field Applications Engineers at the factory, and he said that one of the main causes of element warpage is due to the magnetic field induced by the high current flowing through the heating elements, causing bowing due to the repelling forces of the field.

For context, these are U-shaped elements (like a hairpin) that see upwards of 100A under full load. The cross section of the heated length is only 3mm. I know the “right handed rule of magnetic fields”, but that is about it. For a better understanding, I would like to calculate how much mechanical force the elements actually see at load - e.g., the element legs are repelling each other with a force of 1 oz in.

See 3D model here (thanks to Fusion360)

A fun, complicated problem for which I don’t have the theoretical background. @ChrisGammell - any ideas on resources?

Wow, this is for like induction heaters? I can’t say I’ve ever experienced something like this before.

What would you like to get out of this? A recommendation for simulation software or similar?

And hopefully no hotter as Molybdenum Disilicide melts at 2030C. :wink:

Is this element powered with DC?

I don’t know all of the dimensions of your elements but assuming 30mm spacing and 100mm length a rough calculation gives about 0.007 N of force. But that only takes into account the parallel sections and not the forces within the curved section.

See: Force Between Two Anti-Parallel Currents scroll down to page 53.

I would expect far more warpage from even slightly uneven heating and cooling cycles.

Induction heaters don’t use a heating element, which is known as conduction heating. Induction heaters use a rapidly changing magnetic field to induce eddy currents in the metal being heated, thereby causing the metal to self-heat. While other conductive materials can be heated by induction it is usually used with metals, either to heat and expand metals, or melt them.


@1.21Gigawatts - thank you! This is precisely what I was looking for. I have been traveling, so my apologies for the late response.

The applications we get into typically are AC, not DC. I wonder if that will change the equation, or if since the current is symmetrical, the AC has a net zero effect?

With regards to your note about unevenness - absolutely. The material certainly isn’t perfect, not to mention that they two legs have a symmetry tolerance. At high currents, I would have to believe that this makes a difference.

On a side note, what do you do for a living? I run across very few people who know MoSi2. We have been working with Kanthal for over a decade in a FAE/ sales capacity. Not too many folks outside of industrial heating are even aware of what we do :slight_smile:

@ChrisGammell - I am glad you started this forum!

As I said, I only did a quick calculation and when the result was in the expected range I didn’t check any further. Let me know what results you get.

The calculation doesn’t change for AC or DC but for AC you would want to use RMS current and not peak. With AC I would also expect that if the magnetic field was significant it would be audible.

That depends on the day you ask me. :wink: Mostly I do digital/analog electronics, primarily for embedded systems. I also develop software, both firmware for the embedded systems as well as PC based. Some of the PC software is for industrial automation, coordinating the movements of materials and CNC programs in and out of machines using a laser guided vehicle (LGV), as well as software for industrial robot arms. I also get involved in troubleshooting/repairing the LGV and robot arms. Although I don’t get too involved we also have several induction furnaces for melting/casting various alloys.

I haven’t had a chance to run the numbers yet (trying to work through about a dozen other projects), but I will certainly post them when I get them done. Again, thank you!

I don’t often run across other industrial automation folks, so it is good to meet you! I am based in Ohio - if you ever make it to the Cleveland area I will buy you a coffee. We can commiserate and talk shop :wink:

It’s been a long time since I was in Ohio. These days I live in Australia but I’m from Ontario Canada, just across the lake from Cleveland. :slight_smile:

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