All Questions
92
questions
0
votes
1
answer
320
views
Can both magnetic and electric fields induce current from an EM wave?
I was reviewing a homework problem I completed for class, but I saw different explanation that contradict each other.
My teacher says that this position for the waves is optimal for maximum induced ...
1
vote
0
answers
79
views
Proof $\Delta \vec{E} = \frac{1}{c^2} \frac{\partial ^2\vec{E}}{\partial t^2}$ [closed]
Here's what I'm doing, but I'm not sure if this is correct.
Furthermore, I think $c^2$ is the speed of light, however is $c^2 = (\mu_0\epsilon_0)^{-1}$ as follow?
$$\nabla \times (\nabla \times \vec{...
- 29
1
vote
1
answer
807
views
Hamiltonian classical electrodynamics
After coming across the Lagrangian density of the Maxwell equations
$$
\mathcal{L} = -\frac{1}{4\mu_0} F_{\mu\nu}F^{\mu\nu}-J_\mu A^\mu = \frac{\varepsilon_0}{2}||\mathbf{E}||^2-\frac{1}{2\mu_0}||\...
- 181
3
votes
2
answers
505
views
Faraday's law for a 3-dimensional conductor plate moving in a uniform magnetic field
I am struggling to understand this supposedly simple problem I found in a highschool textbook.
A metallic plate is moving with constant velocity v in a region in which
there is a uniform magnetic ...
- 1,104
1
vote
1
answer
670
views
Changing Electric Field in a Capacitor
A capacitor has circular plates with radius $R$ and is being charged by a constant current $I$. The electric field $E$ between the plates is increasing, so the energy density is also increasing. This ...
1
vote
1
answer
471
views
Is it possible to find potential difference between two point in case of induced EMF created by a time-varying magnetic field?
Q: There is a uniform time varying magnetic field in a circular region as shown in the figure. find out the potential difference across 2 point along an elliptical path as shown in figure.
As far as ...
- 1,022
0
votes
1
answer
236
views
How to find potential difference between two points in a loop in case of motional emf? [closed]
Given below is a question in my physics textbook.
A rectangular frame of wire abcd has dimensions 32 cm×8.0 cm and a total resistance of 2.0 Ω. It is pulled out of a magnetic field B=0.02 T by ...
- 1,022
1
vote
2
answers
139
views
Motion of Test Charge in EM Field [closed]
I have a negative infinite sheet of charge moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ with mass $m$ moves at a constant velocity $v$.
My Question is simple: How will the test ...
- 313
0
votes
1
answer
534
views
Understanding why $\frac{\partial (F_{\mu \nu} F^{\mu \nu})}{\partial (\partial_\lambda A_\beta)}=4 F^{\lambda \beta}$ in Maxwell's Equations [duplicate]
In trying to derive Maxwell's equations from
$$S=\int d^4 x\left(-\frac 1 4 F_{\mu \nu}F^{\mu \nu}\right)$$
Where
$$F_{\mu \nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$$
I'm trying to show that
$$\frac{\...
- 394
3
votes
3
answers
2k
views
Simple derivation of the Maxwell's equations from the Electromagnetic Tensor
Lets start by considering the electromagnetic tensor $F^{\mu \nu}$:
$$F^{\mu \nu}=\begin{bmatrix}0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & ...
- 4,577
0
votes
2
answers
287
views
Interpreting discontinuity in the Poynting vector
An infinite cylinder of radius R has a uniforme current distribution through its surface $\vec \kappa (t)=\kappa(t)\vec \phi$. Find a) the magnetic field generated by the distribuition, b) the induced ...
- 548
2
votes
1
answer
67
views
$\vec H$ calculation, given $\vec J$, exercise confusion [closed]
I would like to calculate $\vec H $ at every point, given the following pattern (which extends infinitely at $x$ and $y$ directions).
(we are viewing at $xz$ plane)
$$
\vec J(x,y,z)=
\begin{cases}
\...
- 161
1
vote
2
answers
597
views
Lagrangian for the Maxwell equations
In his book 'Classical Electrodynamics' Kurt Lechner wants to find a Lagrangian $\mathcal{L}$ so that the Euler Lagrange equations
$$\partial_\mu\frac{\partial\mathcal{L}}{\partial(\partial_\mu A_\nu)}...
- 57
0
votes
0
answers
186
views
Maxwell's equations in vacuum - EL in tensor notation [duplicate]
Following David Tong's great lecture notes on QFT I've got struggling with the following steps he did. Can someone explain the steps between those three lines?
1.1.3 A final Example: Maxwell's ...
1
vote
3
answers
13k
views
Deriving the wave equation for electromagnetic waves
I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this:
The electromagnetic wave equations are given ...
- 87