How to find motional emf w/o an equation for mag field?

[sequoiasprout]

Homework Statement

I need to code (in python) a simulation of a magnet dropping through a metal tube, demonstrating Faraday's law.

Relevant Equations

\oint_C {E \cdot d\ell = - \frac{d}{{dt}}} \int_S {B_n dA}

So I am tackling this by iterating over small rings, but I don't know how on earth I can write a function to calculate the flux through one of those ring's surface area. How can I use the derivative of a function I don't have an expression for? There must be some approximation I can make... but I don't know what it is.

 

[renormalize]

There must be some approximation I can make... but I don't know what it is.

Take a look at this reference, which derives the terminal velocity of a magnet falling through a copper tube and compares the result to experiment:
https://iopscience.iop.org/article/10.1088/1757-899X/810/1/012042/pdf

 

[sequoiasprout]

Thank you- but this won't work for what is asked of me. Interesting though!

 

[renormalize]

Thank you- but this won't work for what is asked of me. Interesting though!

Can you be more specific as to why it won't work?

 

[sequoiasprout]

Can you be more specific as to why it won't work?

I can't just take a function someone else made

 

[renormalize]

I can't just take a function someone else made

Of course not, but you can read and understand the approach the authors use to obtain the magnetic flux through the rings and then apply Faraday's Law to find the force on the falling magnet. With that understanding you should be able to derive the appropriate results for yourself and develop code for it.

 

[berkeman]

Thread is locked temporarily for some admin stuff...

 

[berkeman]

@sequoiasprout -- please respond to my latest DM. Thank you.