2
votes
1answer
108 views

How to transform material permittivity tensor from Cartesian coordinates to another orthogonal coordinate system?

I have a material specified by a permittivity tensor written in Cartesian coordiantes: $$\begin{pmatrix} \epsilon_{xx} & \epsilon_{xy} & \epsilon_{xz}\\ \epsilon_{yx} &\epsilon_{yy} ...
5
votes
3answers
125 views

Integral in different coordinate systems

In Griffiths' electrodynamics book, he uses the equation, $$\nabla^2\mathbf{A}=-\mu_0 \mathbf{J},$$ to state that $$\mathbf{A}(\mathbf{r}) = ...
2
votes
1answer
167 views

Expression of electrostatic field

An electrostatic field is characterized by the fact that it depends only by $r$, isn't it? If it is true, I don't understand why this expression, given in cylindrical coordinates, $${\bf ...
0
votes
2answers
448 views

Electric Dipoles and Spherical Coordinates

I've become confused over the use of spherical coordinates when working with dipole moments. It would probably be best o use an example to show where I'm confused. If we have a pure dipole, with a ...
1
vote
1answer
268 views

Electromagnetic Tensor in Cylindrical Coordinates

I understand that the Electromagnetic Tensor is given by $$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & ...