5
votes
Accepted
When we solve the Maxwell equations for $(\phi,{\bf A})$ in a gauge, will the solution $(\phi,{\bf A})$ automatically obey the gauge condition?
This was stated in a comment, but I wish to make it really clear.
It is not sufficient to look for potentials merely satisfying
$$
\Box \mathbf A = -\mu_0 \mathbf J \\ \; \\
\Box \phi = -\frac{\rho}{\...
- 55.9k
4
votes
When we solve the Maxwell equations for $(\phi,{\bf A})$ in a gauge, will the solution $(\phi,{\bf A})$ automatically obey the gauge condition?
This is a very important issue that is usually overlooked in almost all books even if it being of fundamental relevance in my view. Also with a great impact on the quantization procedure. (Also for ...
- 67.9k
3
votes
Accepted
Do chargeable batteries break the third law of newton?
Assume that electrons are at rest inside a battery. Or if they move, they do so equally in all directions, so the net momentum is $0$. Also assume that they leave one battery terminal with some ...
- 34.9k
3
votes
Accepted
The magnetic force is conservative when the magnetic field is static, what is its potential function then?
This result that:
$$
F = -\nabla U
$$
if $F$ is a conservative forces:
$$
\oint F\cdot dx = 0
$$
only works when they only have a spatial dependence. It does not apply to the magnetic force which also ...
- 8,712
2
votes
When we solve the Maxwell equations for $(\phi,{\bf A})$ in a gauge, will the solution $(\phi,{\bf A})$ automatically obey the gauge condition?
In the particular (Lorentz) gauge that you mentioned, indeed the gauge is satisfied at all times. This can be proven by first writing an equation of motion for the "gauge function",
$$ \...
- 21
2
votes
Maxwell stress tensor for electromagnetic wave
four years later you might not be that interested in the answer, but better late than never.
The way you write your waves is right and convenient, so I'll work with that notation.
$$\vec{E} = (E_1\...
2
votes
I Bring 1 kg of Iron to a Flux Density of 1 T. How Much Energy Does That Take?
Usually we can answer questions like this using $ \frac{U}{V} = \frac{B^2}{2 \mu} $ (magnetic energy stored per unit volume), but since iron is nonlinear and ferromagnetic, we need to use its ...
- 73
2
votes
Accepted
Why should the shape of the surface affect the flux in Faraday's law?
My bad - some ambiguous language in the proof really made things confusing.
Most sources will use the term 'time-dependent surface' to mean that the surface is changing (i.e. changing shape and/or ...
- 163
1
vote
Accepted
Lenz's law in supercoductors: What happens if a superconducting ring approaches a bar magnet?
No. We can think for example of the ring suddenly in free fall, from an initial zero velocity. In $t = 0$ there is a force $F = mg$ acting on it. But, as the relative velocity with respect to the ...
- 15.4k
1
vote
Accepted
How to write equation of oscillating electric field?
The wave vector $\vec{k}$ is in the same direction as the wave is travelling. Since you have been given a unit vector for the direction, then $\vec{k}$ is just $k$ multiplied by that unit vector.
The ...
- 126k
1
vote
Accepted
Confusion about energy transport in a circuit
The wave "knows" where the bulb is because the EM field is directed by the wires to the bulb: The H-field surrounds the wire, while the E-field is between the wires.
Experimentally, there is ...
- 17.2k
1
vote
What is the literal meaning of displacement current?
The reason for the name is historical. Maxwell used this name in the first volume of his Treatise to indicate what we presently call the electric displacement field or electric induction field and ...
1
vote
What is the literal meaning of displacement current?
As stated in the wikipedia article: at the time Maxwell named it that way the name seemed fitting to him.
When the physics community adopted Maxwell's theory of electromagnetism (which actually took ...
- 19.5k
1
vote
Accepted
Are $E_i A_j + E_j A_i$ components of a tensor?
From your remark about the electric field not being a tensor itself, I presume you are referring to Lorentz tensors (rather than tensors in three-dimensional space). The quantities $E_{i}A_{j}$ are ...
Buzz♦
- 15.4k
1
vote
When exactly does a change in $E$ or $B$ result in an electromagnetic wave?
There are two separate issues here:
what kind of electromagnetic fields constitute "waves" or "radiation"?
how does the field of an inertially moving point charge arise, and why ...
- 55.9k
Only top scored, non community-wiki answers of a minimum length are eligible