Okay, the title is promising something big. I'm sorry, it's probably not big, but it does seem important, although for some it will be unsignificant, I suppose it depends on your interests in physics:(adsbygoogle = window.adsbygoogle || []).push({});

So if you have an infinite plane with current density J (current per meter width) (say pointing up in the y direction, in the xy-plane), you have a magnetic field independent of distance, pointing in the +/-x direction (dependent on which side) with formula:

[tex]B = \frac{\mu J}{2}[/tex]

This is easily derived from the Ampère-Maxwell law (Bds = mu*I will suffice).

But what if we use the general result that if we haveone(infinite) conducting wire with current I, the magnetic field at a distance a is:

[tex]B = \frac{\mu I}{2 \pi a}[/tex]

Then if we go back to our infinite J-plane, and we fix ourselves on a certain point on the z-axis looking at the infinite plane, say (0,0,d), we can say a dx-segment of the plane contributes a dB field with

[tex]dB = \frac{\mu J dx}{2 \pi \sqrt(d^2+x^2)}[/tex]

since dI = Jdx (from the definition of J) and we use the fact that the distance 'a' from a certain dI to the fixed point on the z-axis is a = sqrt(d² + x²) with d the distance to the closest dI.

However, taking the integral from x = - infinity .. infinity, it diverges!

Why can't I calculate it this way?

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# Contradiction in Maxwell?

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