Key Equations

Permeability of free space	$μ_{0} = 4 π \times 10^{−7} T \cdot m/A$
Contribution to magnetic field from a current element	$d B = \frac{μ_{0}}{4 π} \frac{I d l sin θ}{r^{2}}$
Biot–Savart law	$\vec{B} = \frac{μ_{0}}{4 π} \int_{wire} \frac{I d \vec{l} \times \hat{r}}{r^{2}}$
Magnetic field due to a long straight wire	$B = \frac{μ_{0} I}{2 π R}$
Force between two parallel currents	$\frac{F}{l} = \frac{μ_{0} I_{1} I_{2}}{2 π r}$
Magnetic field of a current loop	$B = \frac{μ_{0} I}{2 R} (at center of loop)$
Ampère’s law	$\oint \vec{B} \cdot d \vec{l} = μ_{0} I$
Magnetic field strength inside a solenoid	$B = μ_{0} n I$
Magnetic field strength inside a toroid	$B = \frac{μ_{o} N I}{2 π r}$
Magnetic permeability	$μ = (1 + χ) μ_{0}$
Magnetic field of a solenoid filled with paramagnetic material	$B = μ n I$