Production of the magnetic field from 3-phase currents

In summary, the conversation discusses deriving the equation for the magnetic field intensity at the center of three coils with 3 phase currents separated by 120 degrees. The equations for the three currents and the magnetic field intensity equation are given, but the attempt to use Ampere's Law to derive the equation is incorrect. It is mentioned that more information about the geometry of the coils is needed to accurately find the magnetic field intensity at the center.
  • #1
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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?
 
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  • #2
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).
Check here for more info about line integrals.
https://en.wikipedia.org/wiki/Line_integral
More specifically check the section about "Line integral of a Vector field" because H in eq5 is a vector field.

Anyway if you want to find H at the center of the three coils, then you have to make some extra assumptions about the geometry of the coils (for example are they solenoids?), the information from the currents only is not enough.
 
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Related to Production of the magnetic field from 3-phase currents

1. How is the magnetic field produced from 3-phase currents?

The magnetic field is produced by the interaction of the three individual currents in a 3-phase system. Each current creates its own magnetic field, and when combined, they create a rotating magnetic field.

2. What is the purpose of producing a magnetic field from 3-phase currents?

The production of a magnetic field from 3-phase currents is essential for the operation of electric motors, generators, and other equipment that rely on magnetic fields for their function.

3. How is the direction of the magnetic field determined in a 3-phase system?

The direction of the magnetic field is determined by the direction of the individual currents in the system. The right-hand rule is often used to determine the direction of the magnetic field based on the direction of the current.

4. What factors affect the strength of the magnetic field produced from 3-phase currents?

The strength of the magnetic field is affected by the magnitude of the currents, the distance between the currents, and the angle between the currents. The number of turns in the coils and the type of material used for the coils can also impact the strength of the magnetic field.

5. Can the magnetic field produced from 3-phase currents be controlled?

Yes, the magnetic field can be controlled by adjusting the magnitude and direction of the currents, as well as the distance and angle between the currents. Different types of materials and coil configurations can also be used to manipulate the magnetic field.

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