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Please consider the following;

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?

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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 $.

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  • $\begingroup$ So you are suggesting to use the first equation but calculate Jx as (3*10^-3)A/(0.01m * 0.004m) in A/m^2? $\endgroup$
    – Jesse
    Jun 15, 2015 at 4:57
  • $\begingroup$ Basically your two equations are identical, if you assume a constant current distribution over the thickness. This is, how it is usually done in Hall measurements. $\endgroup$
    – engineer
    Jun 15, 2015 at 5:02

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