Attraction between coaxial solenoids

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Two coaxial solenoids with current flowing in the same direction experience an attractive force due to their magnetic fields, despite initial confusion when applying the right hand rule. The right hand rule indicates that the poles of the solenoids align as N-S / N-S, leading to attraction rather than repulsion. When considering the interaction between a small solenoid and a larger one, the small solenoid may appear to stretch in the magnetic field, altering the perceived direction of the force. Graphical representations can clarify the magnetic interactions, showing that while there may be repulsive forces at certain points, the overall effect is attraction at the ends of the coils. Understanding these dynamics is crucial for accurately predicting the behavior of coaxial solenoids.
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Can anyone help me understand why two coaxial solenoids separated by a distance x, with current flowing in the same direction in each solenoid, would be attracted to each other using the right hand rule?

Im sure they would be attracted to one another (with the current flowing in the same direction, the poles are arranged N-S / N-S), but when i try to use the right hand rule I end up saying that there would be a repulsive force.

Anybody know where I'm going wrong?


Any help appreciated


LB
 
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Let's consider a small solenoid in the magnetic field of a large solenoid. Using the right hand rule we see that the small solenoid is not attracted or repelled, it's streched. (radially)


Let's say the small solenoid is elastic. When it enlarges, the direction of the magnetic field that it's in gradually changes.


So: First we imagine a small solenoid, we are using the right hand rule, our thumb is pointing in the direction of the streching force pulling some part of the solenoid, then we start turning our middle finger away from the axis of the solenoid, our thumb is turning to the appropriate direction.
 
Thank you for the reply, but is there a way you can show that graphically?

I've attached a diagram of why I think using the right hand rule the solenoids would repel if that helps.
 

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There is a repelling force then, let's believe whatewer the right had rule says. But there's an attractive force at the other ends of the coils.

The repelling forces in the picture are actually attractive forces towards the other end of the same coil.(I would advice leaving one coils magnetic field out of the picture)
 
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I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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