# Hall effect -- calculate carrier mobility and density

1. Feb 14, 2017

### Kara386

1. The problem statement, all variables and given/known data
A metallic film has length L=10mm, width W=1mm and thickness t=1$\mu m$. The current is parallel to the long edge and has magnitude $I=0.7A$. Longitudinal voltage is $V=1V$ and it doesn't change with magnetic field. The Hall (transverse) voltage $V_H$ increases at $0.3mV/T$. What is the carrier density and what is the carrier mobility?

2. Relevant equations

3. The attempt at a solution
I'd just like to check what I've done. Not sure whether I have to change something else if I want to infinitesimalise variables, but since all variables but the ones I'm changing are constant I think it's ok.
$V_H = \frac{IB}{tne}$
Where $n$ is charge carrier density. Then I think
$\frac{dV_H}{dB} = \frac{I}{ne}$

That's the step I'm not 100% sure about. If it's ok, then
$n = \frac{I}{e\frac{dV_H}{dB}} = \frac{0.7A}{1.6\times10^{-19} C \times 0.3\times 10^{-3}VT^{-1}}$

Is that right? After that I can just get the mobility $\mu$ from this equation:
$V = \frac{L}{W} \frac{I}{en\mu}$

Thanks for any help!

Last edited: Feb 14, 2017
2. Feb 21, 2017

### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Feb 22, 2017

### ehild

You forgot the thickness t.

4. Feb 22, 2017

### Kara386

I did. Thank you!