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klam997
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Homework Statement
N particles diffuse in one dimension in the potential U(x)=ax2, with a > 0. For example, such a potential could be provided by a line-shaped optical tweezer trap. The particles have the diffusion constant D.
Find the steady-state concentration, C0 (x).
Homework Equations
diffusion equation: dc/dt= D d^2(c)/d(x^2)
Fick's law: j = -D dc/dx
Diffusion concentration in 3 dimensions: c(r,t) = N/ [(4*pi*D*t)^3/2] * e^(-r^2/(4Dt)
Nernst-Planck formula and Nernst relation?
The Attempt at a Solution
I wasn't sure if I needed to use the Nernst-Planck formula or the Nernst relation. I know the flux of the system is zero because the particles are trapped within the potential. Therefore, j=0, dc/dx must be zero. At a steady state, I know that dc/dt is zero. I'm not really sure how I can approach this problem maybe except for adding boundaries conditions at the potential. Any thought or help is greatly appreciated!
Thanks in advance!