# 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.

## Faraday's Law

$$ e = N \frac{d \Phi}{dt} $$

Where \( N \) is the number of turns on the coil.