Tagged Questions
1
vote
1answer
50 views
Regarding Electromagnetic Plane and Maxwell equations
I asked this on the math.stackechange but I was told that it might be a good idea to ask here too since my problem is physics/math! Here is the question:
Hello everybody I am kind of struggling with ...
3
votes
2answers
125 views
Metric coefficients in rotating coordinates
Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric
$$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$
I am trying to compute the metric coefficients under the change of ...
1
vote
1answer
215 views
Is it possible to prove that the curl of a gradient equals zero in this way?
If $(\nabla\times\nabla\Phi)_i = \epsilon_{ijk}\partial_j\partial_k\Phi$, where Einstein summation is being used to find the $i$th component...
Using Clairaut's theorem $\partial_{i}\partial_{j}\Phi ...
2
votes
3answers
212 views
How to get an integral formula for the flux time derivative
$$\frac{d}{dt}\int \limits_{A} \mathbf B d \mathbf A = \int \limits_{A} \left( \frac{\partial \mathbf B}{\partial t} + \mathbf v (\nabla \cdot \mathbf B ) + [\nabla \times [\mathbf v \times \mathbf B ...
1
vote
1answer
126 views
How to decompose a divergence operator
I am reading a paper, and see someone decompose a divergence operator as follows, could someone judge and see if it is correct?
$$\nabla \cdot {\bf{v}} = \left( {{\bf{n}} \cdot \nabla } \right){v_n} ...
1
vote
3answers
838 views
Divergence of $\frac{\vec{r}}{r^2}$
In David J. Griffiths 'Introduction to ELECTRODYNAMICS' , as one the excercize he gave the following problem.
Sketch the vector function: $$
\vec{v} = \frac{\vec{r}}{r^2}
...
4
votes
2answers
163 views
A wonky gravitational potential and its critical points
I have tough problem I am not sure how to solve:
For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and ...
2
votes
2answers
637 views
Electric field at a point from a square surface
I'm trying to determine the electric field at a point P (located on the +Z axis) due to a square of side length [L] and centered at the x-y plane origin. The square has a constant surface density [s]. ...
