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Fri, Feb 11, 2022 One-minute read

Magnetic fields with circled current

Assuming the uniform circled electric current, like I[A], we can calculate the magnetic fields created by that current using Biot-Savart’s law or simply calculation of the vector potential and taking the curl of that potential. Actually, that kind of calculation is not obvious because there is elliptic integral when calculating the field in the entire space.

I will share the result I’ve got down below.


magnetic field by electric circled current


the answer for the field B_r (some physical constants omitted)(K and E are the complete elliptic integral of the first and second kind)

I’m going to prepare the upcoming research.