so suppose i have a wire given parametrically by C(t)=x(t),y(t),z(t), and i run a current of I amps through it. to find the total B field i would sum up the contributions over the length of the wire, and (please tell me if im wrong) the total B field due to the wire at point p=x(adsbygoogle = window.adsbygoogle || []).push({}); _{p},y_{p},z_{p}would be

B=[itex]\frac{mI}{4\pi}[/itex][itex]\int[/itex][itex]\frac{\hat{C}'(t)χ(p-C(t))}{|p-C(t)|^{3}}dt[/itex]

where [itex]\hat{C}'(t)[/itex] is the unit vector tangeant to C and m is the permeability of free space, and the bounds of the integral would be t_{0}and t_{1}where the curve begins and ends.

So heres the problem:

while i was programming to find the trajectory of a charged particle due to a current through the wire, i realized that i need to calculate the integral(numerically) on every time step to find the B field at that point in space. this is very inefficient and, with my computer, impossible. I was wondering if there is any way i can calculate the integral only once and be able to use that to find the magnetic field at all points in space?

thanks.

edit: i just noticed i posted this in the wrong forum can mods please move this?

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# How to limit processing demand simulating electromagnetic trajectory

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