- #1
Coffee_
- 259
- 2
I'm looking for a proof of the following statement at a level an early undergrad would understand:
##J=D \vec{\nabla} \vec{n}## where ##D=\frac{v_{th}l}{3}## with ##l## being the mean free path and ##v_{th}## the thermal agitation velocity, ##J## is the particle current density.
I really did try google a lot but no luck. Either the proof is way too complicated for me to understand or it just tells the results without work. I'm looking for a very raw/approximating derivation that doesn't really have to be formal at all, something that can be understood in like 10 minutes, hard assumptions are allowed. I would really appreciate it if someone who knows where I can find one, could inform me.
##J=D \vec{\nabla} \vec{n}## where ##D=\frac{v_{th}l}{3}## with ##l## being the mean free path and ##v_{th}## the thermal agitation velocity, ##J## is the particle current density.
I really did try google a lot but no luck. Either the proof is way too complicated for me to understand or it just tells the results without work. I'm looking for a very raw/approximating derivation that doesn't really have to be formal at all, something that can be understood in like 10 minutes, hard assumptions are allowed. I would really appreciate it if someone who knows where I can find one, could inform me.