Help with understanding force between two current carrying coils

[Arv]

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 next to each other 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.

The M in dM/dX is the mutual inductance which is the coefficient that
describes the linking flux between the two coils. Why should the force
depend on a gradient in mutual inductance? Can someone offer
an intuvitive explanation for this or perhaps provide a sketch of a proof
which I can work on?

Thanks
Arv

 

[anathema]

ind

Dear Arvind,

Thank you for sharing your project with us. The equation you are referring to, F = I1*I2*dM/dX, is known as the Lorentz force equation and is used to describe the force between two parallel current-carrying conductors. In the case of your coil gun, this equation can be used to calculate the force between the active and passive coils.

To understand the dM/dX part of the equation, it is important to first understand what mutual inductance, M, represents. Mutual inductance is a measure of the coupling between two coils and is directly related to the magnetic field produced by one coil that is linked with the other coil. In other words, it is a measure of how much the magnetic field of one coil affects the other coil.

Now, when we take the derivative of mutual inductance with respect to distance, dM/dX, we are essentially looking at how much the mutual inductance changes with a change in distance between the two coils. This change in mutual inductance is directly related to the change in magnetic field between the two coils, which in turn affects the force between them.

To put it simply, the force between the two coils depends on the change in mutual inductance because a change in mutual inductance results in a change in the magnetic field, which in turn affects the force between the two coils.

I hope this explanation helps you understand the equation better. If you need further clarification or assistance, please do not hesitate to reach out. Good luck with your project!

 

[quicknote]

ind

I can provide some clarification on the force between two current carrying coils. The equation you have mentioned, F = I1*I2*dM/dX, is known as the Lorentz force equation. This equation describes the force experienced by a current-carrying conductor in a magnetic field. In your case, the two coils are acting as conductors and the force is being exerted due to the interaction of their magnetic fields.

The dM/dX term in the equation represents the change in mutual inductance with respect to distance between the two coils. Mutual inductance is a measure of the coupling between two coils and is directly related to the magnetic flux linking the coils. So, when there is a change in the distance between the coils, the mutual inductance also changes, resulting in a force being exerted between the coils.

To understand this better, let's break down the equation. The first part, I1*I2, represents the product of the currents in the two coils. This is the same as the Lorentz force equation. The second part, dM/dX, represents the change in mutual inductance. As the distance between the coils changes, the amount of magnetic flux linking the coils also changes, resulting in a change in mutual inductance. This change in mutual inductance then contributes to the overall force between the coils.

In summary, the force between two current-carrying coils is a combination of the Lorentz force and the change in mutual inductance. I hope this explanation helps you better understand the equation and its relevance to your linear motor project. If you need further clarification, please don't hesitate to ask. Best of luck with your project!