Hi,
I'm getting some confusing results and cant figure out what is wrong
Suppose we have a uniform field
[itex]E=[0,0,E_z][/itex] in a dielectric media.
By [itex]E=-\nabla\psi [/itex] we can deduce that [itex]\psi(x,y,z)=-z E_z[/itex]
But, taking the Laplacian
[itex]\nabla^2\psi=\frac{\partial^2 (-zE_z)}{\partial z^2}=0[/itex]
does not match the results of the Poisson equation
[itex]\nabla^2\psi=-\frac{\rho}{\epsilon_m \epsilon_o}[/itex]
what am I missing?
I'm getting some confusing results and cant figure out what is wrong
Suppose we have a uniform field
[itex]E=[0,0,E_z][/itex] in a dielectric media.
By [itex]E=-\nabla\psi [/itex] we can deduce that [itex]\psi(x,y,z)=-z E_z[/itex]
But, taking the Laplacian
[itex]\nabla^2\psi=\frac{\partial^2 (-zE_z)}{\partial z^2}=0[/itex]
does not match the results of the Poisson equation
[itex]\nabla^2\psi=-\frac{\rho}{\epsilon_m \epsilon_o}[/itex]
what am I missing?