Magnetic Circuits

Magnetic Flux $\mathrm{\Phi }$$\Phi$

Magnetic flux $\mathrm{\Phi }$$\large \Phi$ (measured in $Wb$$\large Wb$) is a measurement of the number of magnetic field lines passing through a surface.

Magnetic Flux Density $B$$B$

Magnetic flux density $B$$\large B$ (measured in $Wb/m^2$$\large Wb/m^2$ or $T$$\large T$) is a measurement of the number of magnetic field lines passing through a perpendicular unit area.

where $A$$\large A$ is the area and $\theta$$\large \theta$ is the angle between the field lines and the surface.

Magnetomotive Force $\mathcal{F}$$\mathcal{F}$

Magnetomotive Force $\mathcal{F}$$\large \mathcal{F}$ (measured in $At$$\large At$) is a measurement of the ability of a coil to produce flux.

where $N$$\large N$ is the number of turns on the coil and $I$$\large I$ is the current passing through the coil.

Permeability $\mu$$\mu$

Permeability $\mu$$\large \mu$ (measured in $H/m$$\large H/m$) is the ability of a magnetic material to support magnetic field development.

Reluctance $\mathcal{R}$$\mathcal{R}$

Reluctance $\mathcal{R}$$\mathcal{R}$ (measured in $At/Wb$$\large At/Wb$) is the obstruction offered by a magnetic circuit to the magnetic flux.

where $l$$\large l$ is the average length of magnetic path, $A$$\large A$ is the cross-sectional area of that path, and $\mu$$\large \mu$ is the permeability of the magnetic material.

Ohm's Law for Magnetic Circuits

Ohm's law for magnetic circuits outlines the following relation ship between the magnetomotive force $\mathcal{F}$$\large \mathcal{F}$, the magnetic flux density $\mathrm{\Phi }$$\large \Phi$ and the reluctance $\mathcal{R}$$\large \mathcal{R}$: