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Magnetic Field To Compress A Spring 
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#1
Jun2812, 06:55 AM

P: 895

Suppose we have a spring with a spring constant of [itex]k[/itex]. And it is attached to a magnet (or electromagnet) as in the following diagram that I've made:
I was wondering if it is possible to write an equation for the magnitude of the magnetic field [itex]\vec{B}[/itex] required to compress the spring? Suppose we want to compress the coil for a specific distance d. All we know is [itex]k[/itex] (or the stiffness of the spring).The red area in the diagram is the electromagnet that can produce a reasonably uniform field of any strength we choose. P.S. I haven't tried this before experimentally, so I'm not sure if this arrangement actually works but I think if a permanent magnet is attached to the other side of the spring, the electromagnet would compress the spring much more easily. Here is the diagram: I'm curious how we can determine the amount of [itex]\vec{B}[/itex] needed to compress the spring. 


#2
Jun2812, 07:15 AM

Mentor
P: 11,617

What compresses the spring in graph 2? Is the spring itself ferromagnetic?
In any way, k alone does not help. 


#3
Jun2812, 08:49 AM

P: 1,969

Otherwise, you need a nonuniform field. The magnetic force depends on the actual configuration of the field (its gradient). So another parameter to consider. 


#4
Jun2812, 07:43 PM

P: 895

Magnetic Field To Compress A Spring
[itex]B= \mu_0 \frac{N}{l} I[/itex] So, how do we relate the gradient of the field that you've mentioned to the spring? 


#5
Jun2912, 07:17 AM

Mentor
P: 11,617

If you know the field gradient everywhere, it should be possible to evaluate the force on the individual parts of the spring  if you know how the spring looks like (will depend on its mass probably its geometry). If you have that, you can approximate your spring as system of a lot small springs with forces in between and maybe take the limit for infinitely small spring elements. In equilibrium positions, the summed forces at every position are 0.
As you can imagine, the general situation is quite tricky. It might be possible to find some effective approximations, but I would really try to test this experimentally first. The permament magnet at the other side simplifies the situation, if you can neglect the magnetic forces inside the spring. In this case, you have a single, positiondependent force F(x) (given by the field gradient and your magnet), and the restoring force kx of the spring. Solving F(x)kx=0 will give you equilibrium positions. 


#6
Jul312, 06:52 PM

P: 895

In order to compress the spring, the force applied to the spring due to the magnetic field must overcome the spring's restoring force. We know what the restoring force would equal to. But what is the equation describing the magnitude of the force [itex]F[/itex] on the the spring due to [itex]\vec{B}[/itex]?



#7
Jul412, 04:25 AM

Mentor
P: 11,617

This depends on your geometry, the field gradient and your attached mass and its own magnetic field. The product of magnetic field and field gradient, integrated over the volume of the mass, should give a good approximation.



#8
Jul412, 07:27 AM

HW Helper
Thanks
P: 5,159




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