# How to implement the form of current density in a Hall Effect related calculation?

Question. A rectangular plate of semiconducting material has dimensions 10mm x 4mm x 1mm. A current of 3 mA flows along the length and a Hall Voltage of 13.6 mV is measured transverse to the current flow when the sample is placed in a field of 1.4 T directed normal to the major surface. Determine the concentration of charge carriers in the material.

Attempt;

I have identified the equation $$E_y = \frac{-J_x }{ne} B_z$$ where $E_y$ is the Hall voltage, $B_z$ the magnetic field strength, $n$ the charge carrier concentration, $e$ is a constant and $J_x$ the x-directed current density.

My question is considering $J_x$ is in terms of $A/m^2$ and not $A/m^3$, how do you incorporate the charge density?

I have seen a similar equation $$E_y = \frac{I }{net} B_z$$ where $t$ is the thickness of the square plate and $I$ the current, but would this still be justifiable in ignoring the other components concerning dimension of the plate?

Current density is defined as electrical charge per unit time for a certain cross-section. Since a cross-section is a two-dimensional entity, it has to be $A / m^2$. In some cases it can be simplified to $A / m$.