# Capacitance by solving Poisson equation

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Lalson Vincent 2020년 2월 7일
댓글: Lalson Vincent 2020년 2월 13일
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 ?

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### 답변(1개)

Ravi Kumar 2020년 2월 7일
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
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Lalson Vincent 2020년 2월 13일
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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R2018b

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