How are the poles of a tapered magnet distributed?

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The distribution of poles in a tapered magnet can be complex, with magnetic field lines not concentrating as strongly at the apex as one might expect. Finite Element Method (FEM) modeling software is recommended for accurately calculating the magnetic force of such magnets. An example FEM model of a conical magnet illustrates this concept effectively. The discussion highlights the importance of using advanced modeling tools for precise magnetic force calculations. Understanding these principles is crucial for applications involving tapered magnets.
vdance
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Personal interests.
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I didn't find the right formula.
How are the poles of a tapered magnet distributed?
Is there any way to calculate its magnetic force?
d.jpg
 
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vdance said:
Is there any way to calculate its magnetic force?
Looks like FEM modeling software is your best bet for finding magnetic force. Below is an example FEM model of a conical magnet that I found online. Note that the magnetic field lines don't concentrate at the apex nearly as strongly as in your hand sketch.

Cone Magnet.jpg

http://dx.doi.org/10.1371/journal.pone.0188015
 
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That's a very clear explanation, thank you!
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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