- #1

Lambda96

- 196

- 68

- Homework Statement
- Calculate the potential and check if it satisfies the poisson equation.

- Relevant Equations
- none

Hi,

I don't know if I have calculated the electric field correctly in task a, because I get different values for the Poisson equation from task b

The flow of the electric field only passes through the lateral surface, so ##A=2\pi \varrho L## I calculated the enclosed charge as follows ##q=\rho_0 \pi R^2 L## then I obtained the following electric field ##E=\frac{\rho_0 R^2}{2 \varrho \epsilon_0 }##

For the potential I got the following ##\phi=\frac{\rho_0 R^2}{2 \epsilon_0} \ln{\frac{\varrho }{R}}##

For the Poisson equation I then get ##-\Delta \phi=\frac{\rho_0 R^2}{2 \epsilon_0 \varrho^2 }##

Unfortunately, I don't know what I've done wrong, which also makes me wonder why the task only says ##4 \pi \rho## without the ##\epsilon_0##

I don't know if I have calculated the electric field correctly in task a, because I get different values for the Poisson equation from task b

The flow of the electric field only passes through the lateral surface, so ##A=2\pi \varrho L## I calculated the enclosed charge as follows ##q=\rho_0 \pi R^2 L## then I obtained the following electric field ##E=\frac{\rho_0 R^2}{2 \varrho \epsilon_0 }##

For the potential I got the following ##\phi=\frac{\rho_0 R^2}{2 \epsilon_0} \ln{\frac{\varrho }{R}}##

For the Poisson equation I then get ##-\Delta \phi=\frac{\rho_0 R^2}{2 \epsilon_0 \varrho^2 }##

Unfortunately, I don't know what I've done wrong, which also makes me wonder why the task only says ##4 \pi \rho## without the ##\epsilon_0##