All Questions
19
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
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
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
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
2
votes
2
answers
767
views
What would Maxwell's Equations be if we had magnetic charges and magnetic currents?
Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
- 1,072
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
3
votes
0
answers
206
views
Confusion in reaction force of Ampere's Force Law [closed]
I am reading Maxwell's "A Treatise on Electricity and Magnetism" and I have some confusion in the following pages:
The element ds is resolved into its components $\alpha$ and $\beta$;and the element ...
- 772
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
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
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
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
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
2
votes
1
answer
381
views
A question on Andrew Strominger's lecture
(I now use the same conventions)
(I think the notations are clear enough if you are familiar with differential geometry. Further, I tagged this post as homework-and-excercises. What is the problem ...
- 3,691