User:Msiddalingaiah/Magnetics

Alex Slocum of MIT has some great design tool spreadsheets.

Basics

• Energy in a magnetic field, Ramo et. al.:

$dU_{H}=\int _{V}^{}H\cdot dB\,dV$

• For linear materials, where

$B=\mu H$

$U_{H}={\frac {1}{2}}\int _{V}^{}B\cdot H\,dV$

$U_{H}={\frac {B^{2}V}{2\mu }}$

$U_{H}={\frac {B^{2}Al}{2\mu }}$

• Force is

$F={\frac {dU_{H}}{dl}}$

$F={\frac {B^{2}A}{2\mu }}$

• Force per unit area (pressure) is

$P={\frac {B^{2}}{2\mu }}$

• In the case of free space (air), $\mu _{o}=4\pi \cdot 10^{-7}{\frac {H}{m}}$:

$P=57.7\,{\frac {lb}{in^{2}}}$ @ B = 1 Tesla

$P=230.8\,{\frac {lb}{in^{2}}}$ @ B = 2 Tesla

• In a closed magnetic circuit:

$B={\frac {\mu NI}{l}}$

• Subsituting above,

$F={\frac {\mu N^{2}I^{2}A}{2l^{2}}}$

To build a strong electromagnet, a short geometry, with large area is preferred. Note that most Ferromagnetic materials saturate around 1-2 Tesla. This occurs at a field intensity of:

$H=20\,{\frac {Ampere\cdot turns}{inch}}$

For this reason, there is no point in building an electromagnet with a higher field intensity.