# Magnetic Circuits

In electrical circuits electric current flows through conductors due to the presence of electric fields. Magnetic "current" or "flux" as it is referred to also results from the movement of charges. This is even the case in permanent magnets, where movement of the charged subatomic particles gives rise to the magnetic flux.

Consider an electromagnet consisting of turns of wire wound around an iron core. If there is no current flowing in the windings, the iron can still form a permanent magnet and have an associated magnetic field. This permanent magnet field can be explained by the electrons orbiting the iron atoms nuclei and by the electrons spinning around an axis. If a current is made to flow in the windings in such a way as to form an added magnetic field in the same direction as that of the already existing permanent magnet field, then more magnetic flux will be apparent than if the iron started off as unmagnetised. For this reason, the magnetic flux in the core material is due to both the current through the windings and the "past history" of the core material itself.

For the reasons explained in the previous paragraph, all materials exhibit magnetic properties.

Electric Circuits | Magnetic Circuits | ||||||||
---|---|---|---|---|---|---|---|---|---|

Electrical Property | Variable Symbol | Unit | Unit Symbol | Dimensional Analysis | Magnetic Property | Variable Symbol | Unit | Unit Symbol | Dimensional Analysis |

Electromotive Force, EMF | E or V | Volts | V | M L^{2} / T^{2}C | Magnetomotive Force, MMF | F or Θ (Theta) | Ampere-Turns | A | C / T |

Current | I | Amps = Coulombs per second | A | C / T | Magnetic Flux | Φ (Phi) | Weber = Volt Second | Wb | M L^{2} / TC |

Resistance | R | Ohms | Ω | M L^{2} / TC^{2} | Reluctance | R | Ampere-Turns per Weber or Inverse Henries | A / Wb or H^{-1} | C^{2} / ML^{2} |

Conductance | G | Siemens | S | TC^{2} / M L^{2} | Permeance | P | Weber per Ampere-Turn or Henries | Wb A^{-1} or H | ML^{2} / C^{2} |

Conductivity | σ (sigma) | Siemens per metre | S m^{-1} | TC^{2} /M L^{3} | Permeability | μ (mu) | Henries per metre | H m^{-1} | ML / C^{2} |

Resistivity | ρ (rho) | Ohm Metres | Ω m | M L^{3} / TC^{2} | Reluctivity | C^{2} / ML | |||

Electric Field | E | Volts per metre | V m^{-1} | M L / T^{2}C | Magnetic Field | H | Amperes per metre | A m^{-1} | C / TL |

Current Density | Amps per square metre | A m^{-2} | C / TL^{2} | Flux Density | B | Tesla = Webers per square metre | T | M / TC | |

Dielectric Susceptability | Siemens per metre | S m^{-1} | TC^{2} /M L^{3} | Magnetic Susceptability | Henries per metre | H m^{-1} | ML / C^{2} |

# Equations

Electric | Magnetic | Notes | |
---|---|---|---|

1 | V = I R | Θ = Φ R | V is voltage in Volts, I is current in Amps, R is resistance in Ohms |

2 | G = 1 / R | µ = 1 / R | Conductance is the inverse of resistance. Reluctance is the inverse of permeance. |

From equations 1 and 2 above we get equation 3:

Electric | Magnetic | Notes | |
---|---|---|---|

3 | I = V G | Φ = Θ µ | |

4 | G = σ A / l | P = µ A / l |