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Anyways, I got into a debate about the effect of the core having an induced current. Someone claimed that it would take hundreds of thousands of years for it to decay. Which, to me, makes no sense since the formula they used was for skin depth, which doesn't even make sense to use here because there is no driving frequency - it's a steady state solenoid. If I'm not mistaken, skin depth is derived from a system with a constant frequency that has "leveled off," that is, that any other induction effects have roughly decayed out and now you have a constant driving frequency as if that is what was happening forever. Correct me on this if I am wrong.

In fact, I'm pretty sure that this person simply calculated the frequency you need to get a skin depth of 1800 km. Which, I'm not sure if that really even makes that much sense given the geometry of the problem.

He took this equation:

He then plugged in the skin depth as the radius of Mars's core, about 1800 km, and solved for omega, claiming that the period you get from omega is the decay time, but as 1/4th since it decays to zero. I think that this calculation is kind of silly, since it just actually tells you the angular frequency (and period) you need to get a skin depth of 1800 km, which if you're talking about a massive current running through a wire with a diameter of 50,000 miles would actually give you an adequate description of what's physically happening. He also used the vacuum permeability, and he used the resistivity of iron.

*I'm looking for people who have solid E&M backgrounds who can solve this problem, at least a simplified version of it, with Maxwell's equations, boundary conditions and the like (which, the person who I was debating with didn't even really seem to have knowledge of).*

I'm pretty sure this is just not how any of this works.

I'm pretty sure this is just not how any of this works.

It seemed that other users also were doing the same calculation, and it's more of an engineer's forum - so, perhaps they're misapplying a shorthand, and they're not doing anything EE related professionally? I'm not sure how physics is taught in engineering, outside of the basic physics classes that they usually take through the physics department, which teach on a much more basic level and lack rigor in comparison to the upper division E&M courses you find in physics (which I am rusty on but have taken).

So, help me out! Do these people actually know something I don't, or am I not crazy in thinking that they're full of it?