Magnetic Field and Flux

Field strength H, flux density B and flux Φ, and the permeability linking them.

Easy

$B = \mu H = \mu_0 \mu_r H \qquad \Phi = B A$

$H$ — magnetic field strength (A/m), set by the current.
$B$ — flux density (tesla, T).
$\Phi$ — flux (weber, Wb).
$\mu_0 = 4\pi \times 10^{-7}$ H/m; $\mu_r$ is the relative permeability (air ≈ 1, silicon steel thousands).

Field around a long straight wire: $B = \dfrac{\mu_0 I}{2\pi r}$ . Inside a long solenoid: $B = \mu_0 n I$ .

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