Help with understanding equation for force Between two current carrying coils

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SUMMARY

The discussion focuses on the force equation for a linear motor based on the coil gun principle, specifically the equations Fx = I1*I2*dM/dX and Fy = I1*I2*dM/dY. The active coil induces a current in the passive coil due to Lenz's Law, resulting in repulsion between the coils. The user seeks clarification on the term dM/dX, which represents the rate of change of mutual inductance (M) between the coils, and its contribution to the force experienced by the system. The relationship between this force and the Lorentz Force equation is also explored.

PREREQUISITES
  • Understanding of Lenz's Law and its application in electromagnetic systems
  • Familiarity with mutual inductance and its role in coil interactions
  • Knowledge of the Lorentz Force equation (F = I*L*B)
  • Basic principles of linear motors and coil gun technology
NEXT STEPS
  • Study the derivation of mutual inductance in coupled coils
  • Explore the relationship between changing magnetic fields and induced currents
  • Learn about the application of the Lorentz Force in electromagnetic devices
  • Investigate advanced topics in linear motor design and optimization techniques
USEFUL FOR

Engineers, physicists, and hobbyists involved in electromagnetic systems, linear motor design, or coil gun technology will benefit from this discussion.

Arv
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Hi

I am currently involved in building a linear motor which is based around the coil gun principle. I am having trouble understanding the equation for force used to desribe the coilgun's action.

namely:
Fx = I1*I2*dM/dX

Fy = I1*I2*dM/dX

Here we are considering two coils of wire, with an rapidly
changing current allowed to flow through one of the coils (The active coil)which in turn induces a current in the nearby 'passive' coil (via Lenz Law). So I1 is the active current and I2 is the passive current.

So bascially u end up with two magnetic poles with same polarity and there is a repulsion action. If the vertical movement is constrained, you are left with horizontal thrust which is what the linear motor makes use of.

I can relate this force equation to physics textbooks' description of force betweentwo parallel current carrying conductors which uses the Lorentz Force equation (F = I*L*B) and Magnetic Field near straight wire (B = mu*I/(2*PI*R) to arrive at F = (mu*I1*I2)/(2*PI*D).

I don't how to explain the dM/dX part.

Can someone help me get from the F = I*L*B description to the
F = I*dM/dX description. Thanks

Arvind.
 
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oh..the M in dM/dX is the mutual inductance..(a coefficient to describe the linking flux between the two coils..coupling). I can see how 'good coupling' can help induce large currents however, i don't understand how its rate of change contributes to force..
 
*Fy = I1*I2*dM/dY
 

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