- #1
DivergentSpectrum
- 149
- 15
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 I am wrong) the total B field due to the wire at point p=xp,yp,zp 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 t0 and t1 where the curve begins and ends.
So here's 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?
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 t0 and t1 where the curve begins and ends.
So here's 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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