Formula: Drude Model
$$\class{red}{j} ~=~ \frac{n \, e^2 \, \tau}{m_{\text e}} \, E$$
$$\class{red}{j} ~=~ \frac{n \, e^2 \, \tau}{m_{\text e}} \, E$$
$$E ~=~ \frac{m_{\text e}}{ n \, e^2 \, \tau } \, \class{red}{j}$$
$$\tau ~=~ \frac{ m_{\text e} }{ n\,e^2 } \, \frac{\class{red}{j}}{E}$$
$$n ~=~ \frac{ m_{\text e} }{ \tau \, e^2 } \, \frac{\class{red}{j}}{E}$$
$$m_{\text e} ~=~ n\,\tau \, e^2 \, \frac{E}{\class{red}{j}}$$
Current Density
$$ \class{red}{\boldsymbol j} $$ Unit $$ \frac{ \mathrm A }{ \mathrm{m}^2 } $$
Electric current density represents the current passing through a cross-sectional area.
Electric field (E field)
$$ \class{purple}{\boldsymbol E} $$ Unit $$ \frac{\mathrm{V}}{\mathrm{m}} = \frac{\mathrm{N}}{\mathrm{C}} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{A} \, \mathrm{s}^3} $$
Applied external electric field causing a current density \(j\). As the E-field increases, the current density also increases.
Mean free time
$$ \tau $$ Unit $$ \mathrm{s} $$
Mean free time is the time that elapses between two collisions. During this time, the electron is accelerated collision-free by the electric field to the drift velocity.
Electron density
$$ n $$ Unit $$ \frac{1}{\mathrm{m}^3} $$
Electron density specifies the number of electrons per volume.
Mass
$$ m_{\text e} $$ Unit $$ \mathrm{kg} $$
Mass of the electron. The rest mass of the electron is: \( m ~\approx~ 9.109 \,\cdot\, 10^{-31} \, \mathrm{kg} \).
Elementary charge
$$ e $$ Unit $$ \mathrm{C} = \mathrm{As} $$The elementary charge is a physical constant and is the smallest, freely existing electric charge in our universe. It has the exact value:
$$ e ~=~ 1.602 \, 176 \, 634 ~\cdot~ 10^{-19} \, \mathrm{C} $$