- #1
Trifis
- 167
- 1
I need a mathematical proof that should indicate the following: The direction of the electric field must be radial, for a spherical charge distribution to remain invariant after applying a rotation matrix to its field.
Analogously how can we prove that the electric field of a infinite cylinder is perpedicular to its surface?
Moreover, consider our augmentation at the boundary value problem of electrostatics. Dirichlet's condition was once more taken as granted, of course there not due to some symmetry but nevertheless the principle remains the same!
In other words, why is the electric field of the symmetric objects the way it is? Is it an experimental result or just the result of a superposition, which could be deducted? After all, all the great consequences of the laws of electrostatics are based on these initial "symmetry" assumptions! E.g. we could not calculate the electric field of a sphere with Gauss's law without "guessing" its direction!
I need maths in order to unravel this symmetry mystery...
Analogously how can we prove that the electric field of a infinite cylinder is perpedicular to its surface?
Moreover, consider our augmentation at the boundary value problem of electrostatics. Dirichlet's condition was once more taken as granted, of course there not due to some symmetry but nevertheless the principle remains the same!
In other words, why is the electric field of the symmetric objects the way it is? Is it an experimental result or just the result of a superposition, which could be deducted? After all, all the great consequences of the laws of electrostatics are based on these initial "symmetry" assumptions! E.g. we could not calculate the electric field of a sphere with Gauss's law without "guessing" its direction!
I need maths in order to unravel this symmetry mystery...