Force of a Magnetic Field on a Magnet

 , where:

F = Force (N)

 = Gradient

m = Magnetic Moment (A*m2)

 = Dot Product

B = Magnetic B-Field (T)

Free Current


 , where:

I = Current (A)

J = Current Density (A/m2)

And the subscripts:

(none) = Total

F = Free

M = Magnetization

P = Polarization

Gauss's Law for Magnetism

 , or

 , where:

 = Divergence

B = Magnetic B-Field (T)

S = Closed 3-D Surface

Hopkinson's Law

Hopkinson's Law for magnetic circuits defines the magnetic reluctance as:

 , where:

R = Magnetic Reluctance (A/Wb)

F = Magnetomotive Force (A)

 = Electric Flux (Wb)

Magnetic Constant (Vacuum Permeability)

The magnetic constant in physics, also known as vacuum permeability or permeability of free space, it uses the symbol mu nought (u0) for the value:

 , where:

 = Magnetic Constant (Magnetic Field Constant), also known as Vacuum Permeability (H/m)

Note that mu naught over four pi also provides a relevant result: