Key Equations

Permeability of free space	${\mu }_0=4\pi \times {10}^{\mathrm{-7}}\text{T}\cdot \text{m/A}$
Contribution to magnetic field from a current element	$dB=\frac{{\mu }_0}{4\pi }\frac{Idl\text{sin}\theta }{r^2}$
Biot–Savart law	$\overrightarrow{B}=\frac{{\mu }_0}{4\pi }{\displaystyle \underset{\text{wire}}{\int }\frac{Id\overrightarrow{l}\times \widehat{r}}{r^2}}$
Magnetic field due to a long straight wire	$B=\frac{{\mu }_{0}I}{2\pi R}$
Force between two parallel currents	$\frac{F}{l}=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}$
Magnetic field of a current loop	$B=\frac{{\mu }_{0}I}{2R}\text{(at center of loop)}$
Ampère’s law	${\displaystyle \oint \overrightarrow{B}}·d\overrightarrow{l}={\mu }_{0}I$
Magnetic field strength inside a solenoid	$B={\mu }_{0}nI$
Magnetic field strength inside a toroid	$B=\frac{{\mu }_{o}NI}{2\pi r}$
Magnetic permeability	$\mu =(1+\chi ){\mu }_0$
Magnetic field of a solenoid filled with paramagnetic material	$B=\mu nI$