No, I can't agree with that without a lot more info. Yes, velocity is defined with respect to some specified inertia frame. Why do you say that the current density does not need to be defined with respect to the test charge?
For example, consider a test charge "T" and a source charge "S" in...
O.k., the notation I used was not clear enough. Sorry. I was hurrying...
The Laplacian can go under the integrals because it operates on the test body's coordinates and the integral is with respect to the source body coordinates. Recall that in electrodynamics there are two different...
I am confused by the definition of current density in Maxwell electrodynamics. Perhaps someone can help me out?
As I understand it, the current density function can be written as
$$ \vec{J} = \rho \vec{v}_S$$
where ρ is the charge density function and v_S is the continuous source charge...
I have read the chapter 12.0 and 12.1 sections you pointed me to. http://web.mit.edu/6.013_book/www/book.html
The author writes: "In Chap. 4, we made $$ \vec{E} = - \nabla \Phi $$ ... Later he writes equation (3) as
$$ \vec{E} = -\nabla \Phi - \partial \vec{A} / \partial t $$.
But your...
This is wonderful input. Thank you.
So let's check Gauss's Law using the definition of E in terms of the scalar and vector potential functions:
$$ \nabla \bullet \vec{E} = -\nabla \bullet \nabla \Phi - \nabla \bullet \partial \vec{A} / \partial t \\
\nabla \bullet \vec{E} = -\nabla^2 \Phi -...
I have an issue with Gauss's Law when it is considered one equation of Maxwell's complete system of equations. I don't have an issue with it when it is a standalone equation, but when it is one of several equations put together to form a complete system of equations, there is an issue.
How is...