# Poissons' equation of find potential

1. Oct 11, 2008

### FourierX

1. The problem statement, all variables and given/known data
Two infinte parallel plates separated by a distance s are at potentials 0 and V_o.
a) Use poisson's equation to find the potential V in the region between the plates where the space charge density is $$\rho$$ = $$\rho_o$$(x/s). The distance x is measured from the plate at zero potential.

2. Relevant equations

$$\nabla$$$$^{2}$$ V = -$$\frac{1}{\epsilon_o}\rho$$

3. The attempt at a solution
I used the Poisson's equation as stated but could not really get logical looking V. Charge densities on the plates are pain in the neck also.

Last edited: Oct 11, 2008
2. Oct 11, 2008

### borgwal

The equation you list under 2., is not Poisson's equation. Poisson's equation will be simple for this case.

3. Oct 11, 2008

### FourierX

thanks brogwal, i resolved my equation, that was blunder. But i am stuck again :(

4. Oct 11, 2008

### borgwal

Hint: is V gonna depend on y and z?

5. Oct 11, 2008

### FourierX

No, V does not depend on y and z. I did not get the hint :c

6. Oct 11, 2008

### borgwal

Just write out the equation for V in the case it depends only on x [you do know what $\nabla^2$ stands for I hope!]. I'm sure you can solve that equation.

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