All Questions
92
questions
26
votes
3
answers
9k
views
Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations
I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
- 6,000
20
votes
3
answers
2k
views
Electromagnetism problem: where does the magnetic field come from?
Consider the following problem:
Consider a plane with uniform charge density $\sigma$. Above the said plane, there is a system of conducting wires made up of an U-shaped circuit on which a linear ...
- 571
13
votes
2
answers
5k
views
Deriving Biot-Savart Law from Maxwell's Equations
As an exercise, I've been trying to derive the Biot-Savart law from the second set of Maxwell's equations for steady-state current
$$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
- 838
8
votes
3
answers
5k
views
Derivation of the speed of light using the integral forms of Maxwell's Equations
Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
- 905
5
votes
2
answers
3k
views
Derivative of the electromagnetic tensor invariant $F_{\mu\nu}F^{\mu\nu}$
The electromagnetic field tensor is $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to calculate the quantity
$$ \frac{\partial(F_{\alpha\beta}F^{\alpha\beta})}{\partial(\partial_{\...
- 661
5
votes
1
answer
122
views
Why do these calculations of EM fields for a magnet and wire loop seem inconsistent?
Suppose you have a conducting circular wire loop and a magnet moving towards each other. They move along the $z$ direction with nonrelativistic constant speed $v$. Let the $B$ field of the magnet in ...
- 145
5
votes
1
answer
570
views
Confusion in Maxwell's derivation of Ampere's Force Law - Part II [closed]
I am reading Maxwell's "a treatise on electricity and magnetism, Volume 2, page 156" about "Ampere's Force Law". I have some confusion in the following pages:
My question is of two parts:
1. ...
- 772
4
votes
1
answer
232
views
Does a homogeneous oscillating electric field produce a magnetic field?
I am working on a homework problem that says an electron in a continuous laser field can be modeled as experiencing a homogeneous oscillating electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}...
- 4,235
4
votes
1
answer
600
views
In plasma physics, why are the motional electric field and the frozen-in-flux condition represented by the same equation? ($E = -u \times B$)
I'm trying to refine my understanding of space plasmas, and feel like there's an intuitive understanding here that I'm just missing.
We commonly refer to a motional electric field in the solar wind. ...
- 43
4
votes
2
answers
2k
views
Neither Biot-savart nor Ampere Law can solve this problem?
I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law.
I want to calculate the magnetic field due to current carrying a circular loop over itself, i....
- 169
3
votes
2
answers
247
views
Using Faraday's law twice
I have trouble understanding Faraday's law when there is an induced current which in turn induces another current in the same circuit. I shall illustrate my confusion with an homework problem and I ...
- 963
3
votes
5
answers
18k
views
How to use Ampere's Law for a semi-infinite wire with current?
Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
- 317
3
votes
1
answer
112
views
Nabla commutation in electromagnetism
I don't know how to work with the 'reversed' dot product operator,
$$v\cdot \nabla$$
I arrived to expressions like this trough doing some calculus, and I don't know how to continue with the calculus ...
- 529
3
votes
1
answer
19k
views
Magnetic field in a capacitor
If in a flat capacitor, formed by two circular armatures of radius $R$, placed at a distance $d$, where $R$ and $d$ are expressed in metres (m), a variable potential difference is applied to the ...
- 2,547
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