Lorentz’s force
\[ \overrightarrow{F}_B = q(\overrightarrow{E} + \overrightarrow{v}\times\overrightarrow{B}) \]
Charge density
\[ nev_d = J = {i\over A} \]
Permeability Constant \[ \mu_0 = 4\pi \times 10^{-7} \si{T\cdot m / A} \]
Hall effect
There is a potential difference when a magnetic field is present in a wire, causing the charges to seperate within the wire. This results in a Hall potential difference \(V = Ed\) where d = width of strip
Circulating particle
\[ r = \frac{mv}{|q|B} \]
\[ f = \frac{|q|B}{2\pi m} \]
Force on a wire
\[ F_B = iL\times B \]
Torque on a coil
\[ \tau = NiAB\sin\theta = \mu \times B \] where \[ \mu = NiA \]
Magnetic field due to current
\[ \dd\overrightarrow{B} =\frac{\mu_0}{4\pi}\frac{i\dd\overrightarrow{s}\times \hat r}{r^2} \hspace{10}\text{(Biot-Savart law)} \]
The magnetic field at distance R from a long straight wire is
\[ B = \frac{\mu_0i}{2\pi R} \]