- #1
issacnewton
- 1,026
- 36
Here is the problem from I.E.Irodov's Basic laws of electromagnetism.
An infinitely large plate made of homogeneous linear isotropic dielectric with dielectric constant
[itex]\epsilon[/itex] is uniformly charged by an extraneous charge (see footnote) with volume density [itex]\rho > 0[/itex].The thickness of the plate is 2a. Find the magnitude of [itex]\mathbf{E}[/itex] and the potential [itex]\varphi[/itex] as functions of distance x from the middle of the plate (assume that the potential is zero at the middle of the plate).
Now the author has given the solution in the book . I am just trying to understand it. He says, "From symmetry considerations it is clear that E=0 in the middle of the plate, while at all other points vectors [itex]\mathbf{E}[/itex] are perpendicular to the surface of the plate"
I am trying to see this from more mathematical arguments using the typical equations involved here.
[tex]\vec{\nabla}\times \vec{E} =0[/tex]
[tex]\vec{\nabla}\times \vec{D}=\vec{\nabla}\times \vec{P}[/tex]
[tex]\vec{\nabla}\bullet \vec{D}=\rho_f [/tex]
How do I proceed ?
footnote: Extraneous charges are frequently called free charges , but this term is not
convenient in some cases since extraneous charges may be not free ( this is author's footnote and I don't really understand what he means by it)
An infinitely large plate made of homogeneous linear isotropic dielectric with dielectric constant
[itex]\epsilon[/itex] is uniformly charged by an extraneous charge (see footnote) with volume density [itex]\rho > 0[/itex].The thickness of the plate is 2a. Find the magnitude of [itex]\mathbf{E}[/itex] and the potential [itex]\varphi[/itex] as functions of distance x from the middle of the plate (assume that the potential is zero at the middle of the plate).
Now the author has given the solution in the book . I am just trying to understand it. He says, "From symmetry considerations it is clear that E=0 in the middle of the plate, while at all other points vectors [itex]\mathbf{E}[/itex] are perpendicular to the surface of the plate"
I am trying to see this from more mathematical arguments using the typical equations involved here.
[tex]\vec{\nabla}\times \vec{E} =0[/tex]
[tex]\vec{\nabla}\times \vec{D}=\vec{\nabla}\times \vec{P}[/tex]
[tex]\vec{\nabla}\bullet \vec{D}=\rho_f [/tex]
How do I proceed ?
footnote: Extraneous charges are frequently called free charges , but this term is not
convenient in some cases since extraneous charges may be not free ( this is author's footnote and I don't really understand what he means by it)