Electromagnetism

Flux Density:

$$B = \frac{\Phi}{A}$$

Where $$B$$ is the flux density (Teslas, $$T$$), $$\Phi$$ is the magnetic flux (Webers, $$Wb$$), $$A$$ is the cross-sectional area.

Permeability:

$$\mu _r = \frac{\mu}{\mu _o}$$

Where $$\mu _r$$ is the relative permeability ($$Wb/Am$$), $$\mu$$ is the permeability of the measured material, $$\mu _o$$ is the permeability of free space, $$4 \pi \times 10^{-7} Wb/Am$$.

Reluctance:

$$\Re = \frac{1}{\mu A}$$

"Resistance" to flow of magnetic flux. Analogous to resistance, where magnetic flux is analogous to current.

Magnetomotive Force (MMF):

$$\Phi = \frac{\mathfrak{F}}{\Re}$$

Magnetic equivalent of Ohm's law. Where $$\mathfrak{F}$$ is the magnetomotive force needed to overcome the reluctance $$\Re$$.

The strength of magnetomotive force is measured in Ampere turns ( $$At$$), and related to the number of turns and the current.

$$\mathfrak{F} = NI$$
$$\Phi = \frac{NI}{\Re}$$

Field Intensity:

The longer the magnetic path, the greater the MMF required to drive the flux.

$$H = \frac{\mathfrak{F}}{l}$$
$$B = \mu H$$

Where $$H$$ is the magnetising force, or field intensity.

Electromagnetic Force

$$F = BIl$$

Where $$F$$ is the induced force, $$B$$ is the flux density or field strength, $$I$$ is the current through the wire, $$l$$ is the length of wire affected.

Generator EMF

$$e = Blv$$

Where $$e$$ is the electrical power output (Volts, $$V$$), $$B$$ is the magnetic flux or field strength, $$l$$ is the length of wire affected, $$v$$ is the velocity of the wire through the field.

$$e = N \frac{d \Phi}{dt}$$
Where $$N$$ is the number of turns on the coil.