# 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 12 Feb 2020
Thanks Again.
I am now able to find the electric field now.
Now i need to integrate the squre of electric field over volume to find the energy stored. I have used trapz to integrate it. But its not giving the required solution.
Energy = integral (1/2 * Epsilon * E^2) dV.
Ravi Kumar on 12 Feb 2020
I don't have good suggestion without knowing what is the required solution. My guess is that you might be encountering under resolved results, try increasing mesh density.
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 ?