# Production of the magnetic field from 3-phase currents

PhysicsTest
TL;DR Summary
Magnetic field equation based on the 3 phase currents.
This is not a homework problem, I want to calculate the equation of the magnetic field intensity from the 3 phase currents separated by 120Degrees. The 3 currents are
##I_{{aa}^{'}} = I_M\sin \omega t ; -> eq1 \
I_{{bb}^{'}} = I_M\sin(\omega t - 120); -> eq2\
I_{{cc}^{'}} = I_M\sin(\omega t -240); -> eq3
##
The current in coil ##{{aa}^{'}}## flows into the ##a## end of the coil and out the ##{{a}^{'}}## end of the coil. It produces the magnetic field intensity ##H_{{aa}^{'}}(t) = H_M\sin(\omega t) \angle 0## -> eq4;
I wanted to derive eq1. The equation from the book about the magnetic field intensity
##\oint H.dl = I_{net} -> eq5; ##
My attempt is
##H = \frac{dI_{{aa}^{'}}} {dl} ->eq6 ## substitute eq1 into eq6.
##H = \frac{dI_M\sin \omega t} {dl} -> eq7 ##
But i don't see the equation 6 in terms of ##l##, how to solve this and derive equation 4?

• Delta2

Homework Helper
Gold Member
You have misinterpret Ampere's Law (eq5), the integral that appears there is not a "simple" integral but a line or path integral around a closed curve. So (eq6) simply doesn't hold (it would hold if that integral was a simple integral as i said).
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