# Capacitance by solving Poisson equation

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Lalson Vincent on 7 Feb 2020
Commented: Lalson Vincent on 13 Feb 2020
Hi ,
I want to find the capacitance by solving the Poisson equation. I solved the voltage potential and was able to plot the voltage potential. I want to find the electric potential and energy from from the voltage
First i have to find electric potential which is gradient of voltage.
Then i have to find the energy Energy = integral(1/2 * Epsilon * E^2) over volume.
Can you help me find the gradient of voltage and then the energy ?

Ravi Kumar on 7 Feb 2020
If you setup the problem using PDE Toolbox, look here for example, then you get the gradients of the solution in the results.
Regards,
Ravi
Lalson Vincent on 13 Feb 2020
Required solution is the capacitance of the system with the applied voltage.
Energy = integral (1/2 * Epsilon * E^2) dV = 1/2 * C * V^2
Capacitance = Energy / (1/2 * V^2).
Tried with finer mesh. Looks like, trapz is not the correct method. Is there any way to integrate this ?

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