Magnetics

Magnetic field in a solenoid
B = µ₀µᵣNI/h
B = µ₀µᵣH
H = NI/h
B is the magnetic field in teslas or
   Webers per square meter
H is magnetic field strength in Amps/m
h is length of solenoid in meters
N is number of turns
I is current in amps
µ₀ is the magnetic constant
    1.2566e-6 H/m (or T·m/A)
µᵣ is the relative permeability of the core material
  5000 for pure iron
  1 for air or vacuum
  600 for nickel
μ (µ₀μᵣ) the permeability of the material of the core
A flux density of one Wb/m² is one tesla.
1 Wb = 1T·1m²

for a short solenoid, with radius > length
B = µ₀µᵣNI / 2R
R is radius of coil

Energy in an inductor in Joules
E = ½LI²

Magnetic field in a wire (Ampere's Law)
B = µ₀I/2πr in Tesla
where r is the measurement point from the wire
I is current in amps
µ₀ is the magnetic constant
    1.2566e-6 H/m (or T·m/A)
Direction of the magnetic field is determined by the right hand
 rule, thumb points in direction of conventional current and
 curl of fingers indicates direction of field.

Force on a current carrying wire in a magnetic field is
F = ILB
B is magnetic field in tesla
I is current in amps
L is length of the wire

Ampere's Force law, force between two wires with current.
Fm = 2KaI₁I₂/r
Fm is force per unit length in N/m
ka is magnetic force constant = µ₀/4π = 1e-7 N/amp²
r is spacing of the wires in meters
I₁ and I₂ are the DC currents in the wires in amps
If the currents flow in the same direction, the force points
 towarda the other wire

Force between two magnetic poles
If both poles are small enough to be represented
as a single points then they can be considered to
be point magnetic charges. Classically, the force
between two magnetic poles is given by
F = μ•qm1•qm2 / r²
where F is force in newton
qm1 and qm2 are the magnitudes of magnetic poles in
  amp-meter
μ is the permeability of the intervening medium
  in tesla meter per ampere, henry per meter
  or newton per ampere squared
r is the separation in meter

Inductance of a solenoid
L = µ₀µᵣN²A/Ln
Ln is length in meters
A is cross-sectional area in meters²
N is number of turns
µ₀ is the magnetic constant
    1.2566e−6 H/m (or T·m/A)
µᵣ is the relative permeability of the core material
Inductance of a wire
L = Ln(200e-9)(ln (4(Ln/d) – 1))
E = ½LI² Energy in an inductor

Magnetics Universal Transformer EMF Law
If the flux in the core is purely sinusoidal, the
relationship for either winding between its rms voltage
Erms of the winding, and the supply frequency f, number
of turns N, core cross-sectional area A and peak
magnetic flux density B is given by the universal EMF
equation: Erms = 4.44fNAB