User:Msiddalingaiah/Magnetics

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Alex Slocum of MIT has some great design tool spreadsheets.

[edit] Basics

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

dU_H = \int_{V}^{} H \cdot dB \, dV

  • For linear materials, where

B = μH

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.