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

$$B = \mu H$$

$$U_H = \frac{1}{2}\int_{V}^{} B \cdot H \, dV$$

$$U_H = \frac{B^2 V}{2 \mu}$$

$$U_H = \frac{B^2 A l}{2 \mu}$$


 * 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:

$$B = \frac{\mu N I}{l}$$


 * Subsituting above,

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

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.