5
votes
2answers
178 views

When can I use $\wedge$ instead of curl?

It seems in some circles the wedge product is used in preference to curl. I have a basic understanding of Green and Stokes' formula, I wish to use the $\wedge$ notation from now on. Can someone tell ...
1
vote
1answer
33 views

How you call the constant $\alpha$ within the heat equation in general and in terms of electromagnetism?

The heat equation or diffusion equation does contain a constant $\alpha$. $$\frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$$ How is it called? I'm interested in a general name which can be ...
4
votes
2answers
129 views

Conventions regarding partial derivatives

Look at this expression: $$\frac{\partial}{\partial t} (V-\mathbf{v}\cdot\mathbf{A}).$$ This expression occurs in Griffiths EM book (4th ed, p.444). $V=V(\mathbf{r},t)$is the scalar potential, ...
3
votes
1answer
77 views

What does $\int_C V \,d\mathbf{l}$ mean?

What does $$\int_C V \,d\mathbf{l}$$ mean? I initially thought it was simply a line integral around $C$, that is, if $\mathbf{r}: [0,1] \longrightarrow \mathbb{R}^3$ is a paremetrization of $C$, then ...
5
votes
0answers
112 views

Is it correct to sum over either index of the metric the same way?

I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} ...
0
votes
1answer
2k views

Mutual Inductance and the Dot Convention

Can anyone please explain me, the dot convention in coil systems (Mutual and self inductance) with some related images to understand..?
1
vote
2answers
283 views

Notation of plane waves

Consider a monochromatic plane wave (I am using bold to represent vectors) $$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$ $$ ...