https://www.youtube.com/watch?v=xTwDZJG_W9w
In this video at 9:12 it details the potential energy of an induced dipole
Specifically $$U=-mBcos\theta=(\frac{\chi V}{\mu_0}B)Bcos\theta$$ & $$F_z=\frac{3\mu_0\chi V m_m}{2\pi^2}\frac{1}{z^7}$$
- What would the full derivation be to get the power of 7 fall off?
- Is this accurate for most cases?
- Example: If I had a copper bullet(spherical musket like) travelling at a powerful spherical neodymium magnet; would I just use the $U$ & $F_z$ against the Newtonian $F=ma$ & $K_e=\frac{1}{2}mv^2$ respectively?
- The Force is simply the 2 magnetic moments multiplied together with a 7th power fall off?(just looking for confirmation for the simplification)
- Stability regions are defined as $$F=0=F_{gravitational}+F_{kinetic}-F_{diamagnetic/superconductive}$$ ?
- Are these equations valid for Km scales? Even thousands of Km?(Car scale to planet/star scale)
- Can I use these equations to plot the positions of diamagnetic objects vs magnetic objects in space in a similar fashion to the gravitational & kinetic equations?(or are there better equations for that?)
