Formula: Hall Effect Hall Voltage Electric current Magnetic flux density (B-field) Thickness Charge carrier density (Particle density)
$$U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d}$$
$$U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d}$$
$$I ~=~ \frac{ U_\text{H} \, n \, q \, d }{ \class{violet}{B} }$$
$$\class{violet}{B} ~=~ \frac{ U_\text{H} \, n \, q \, d }{ I }$$
$$d ~=~ \frac{1}{n \, q} \frac{ I \, \class{violet}{B} }{ U_\text{H} }$$
$$q ~=~ \frac{1}{n \, d} \frac{ I \, \class{violet}{B} }{ U_\text{H} }$$
$$n ~=~ \frac{I \, \class{violet}{B}}{q \, d} \, \frac{1}{ U_\text{H} }$$
Hall Voltage
$$ U_{\text H} $$ Unit $$ \mathrm{V} $$
This voltage is generated between the two ends (e.g. of the metal plate used in the Hall effect).
Electric current
$$ \class{red}{\boldsymbol I} $$ Unit $$ \mathrm{A} $$
Electric current generated by applying a voltage (not Hall voltage!) along the Hall plate. The charge carrier current is deflected in the magnetic field to the upper or lower part of the Hall plate.
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} $$
Magnetic flux density determines the strength of the magnetic field applied orthogonally to the Hall plate. The larger \( \class{violet}{B} \), the greater the deflection of the charges, resulting in a larger Hall voltage.
Thickness
$$ d $$ Unit $$ \mathrm{m} $$
Thickness of the Hall sample in which the Hall effect is investigated. This can be, for example, the thickness of a rectangular metal plate.
Electric charge
$$ q $$ Unit $$ \mathrm{C} $$
Electric charge of a charge carrier. If the current consists mainly of electrons, then: \( q ~=~ -e \) (\(e\) is the elementary charge). And in the case of hole conduction: \( q ~=~ +e \).
Charge carrier density
$$ n $$ Unit $$ \frac{1}{\mathrm{m}^3} $$
Charge carrier density indicates the number of charge carriers per volume. The greater the charge carrier density, the lower the Hall voltage.