Hall effect -- calculate carrier mobility and density

[Kara386]

Homework Statement

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?

Homework Equations

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!

 

[ehild]

Homework Statement

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?

Homework Equations

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
$\frac{dV_H}{dB} = \frac{I}{ne}$

You forgot the thickness t.

 

[Kara386]

You forgot the thickness t.

I did. Thank you!