Force Between Two Concentric Solenoids

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In summary, the conversation discusses the scenario of two solenoids, one with a time-varying current and the other coaxial and connected to the first, and the possibility of calculating the magnetic force on the second solenoid. The question is whether this can be done analytically or if it requires numerical solving, and whether it would still hold true if the solenoids were thin shells instead of having finite thickness.
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Imagine a finite length solenoid with outer radius R1 and inner radius R2. This solenoid has a time-varying current going though it. This solenoid is also fixed so that it cannot move. Now imagine another solenoid, coaxial with the first, with its outer radius equal to R2 such that it can slide in and out of the first solenoid. The ends of this solenoid are connected together and no current is being externally applied to it. The only current going through it is the induced current from the first coil. My question is, would it be possible to calculate the magnetic force on this solenoid? Or is this a problem that would need to be solved numerically?
 
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My question can be simplified so that both solenoids are a thin shell instead of having a finite thickness. I'm just wondering how one solenoid within another reacts.
 

FAQ: Force Between Two Concentric Solenoids

What is the force between two concentric solenoids?

The force between two concentric solenoids is a phenomenon where two cylindrical coils are placed one inside the other, and an attractive or repulsive force is experienced between them due to the interaction of their magnetic fields.

What is the formula for calculating the force between two concentric solenoids?

The formula for calculating the force between two concentric solenoids is F = μ0N1N2I1I2A/l, where μ0 is the permeability of free space, N1 and N2 are the number of turns in each solenoid, I1 and I2 are the currents flowing through each solenoid, A is the cross-sectional area of the solenoids, and l is the distance between the two solenoids.

How does the distance between the solenoids affect the force?

The force between two concentric solenoids is inversely proportional to the distance between them. This means that as the distance between the solenoids increases, the force decreases and vice versa.

Is the force between two concentric solenoids always attractive?

No, the force between two concentric solenoids can be either attractive or repulsive depending on the direction of the currents flowing through the solenoids. If the currents are flowing in the same direction, the force will be attractive, and if they are flowing in opposite directions, the force will be repulsive.

Can the force between two concentric solenoids be increased?

Yes, the force between two concentric solenoids can be increased by increasing the number of turns in the solenoids, increasing the current flowing through the solenoids, or decreasing the distance between the solenoids.

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