All Questions
Tagged with electromagnetism homework-and-exercises
1,550
questions
2
votes
1
answer
75
views
Question about the deduction of Hamiltonian of Schwinger model
In Sidney Coleman's paper More about massive schwinger model (PDF). Discuss about some property of massive (1+1)D QED model, In page 5 of this paper, Coleman derive the following Hamiltonian of ...
1
vote
0
answers
35
views
Derivation of pressure balance equation for a toroidal geometry [closed]
Derivation of pressure balance equation in toroidal geometry
$$
\boxed{
\frac{\mathrm{d}p}{\mathrm{d}r} + \frac{\mathrm{d}}{\mathrm{d}r} \left( \frac{B_{\phi}^2}{2\mu_0} \right) + \frac{B_{\theta}}{\...
- 494
0
votes
1
answer
109
views
Multipole expansion along a ring [closed]
I'm supposed to calculate the behavior of the electrostatic potential $V$ at large distances $|r| \gg a$ for the following linear charge density along a ring of radius $a$:
$$\rho(r,\psi, z) = \frac{q}...
- 287
0
votes
1
answer
58
views
How can a changing electric current in the Earth's magnetic field be used to raise your orbit?
Imagine you are on a space station orbiting the Earth. You are subject to small amounts of atmospheric drag, so you must occasionally boost your orbit higher, as it decays over time.
Now imagine you ...
- 755
0
votes
2
answers
205
views
How to determine the electric and magnetic fields from $*F=q\sin \theta d\theta \wedge d\phi$?
I have the 2-form $*F=q\sin \theta d\theta \wedge d\phi$, how can I determine the eletric and magnetic fields from that?
I have tried wrtting F in the vector potential form for them finding the ...
- 346
2
votes
1
answer
855
views
What will happen to the bulb of the circuit after closing the switch? [closed]
Say it connects a bulb with the circuit below, with the switch $S$ open. Every cable has negligible resistance and the battery has no internal resistance.
What happens to the brightness of the bulb ...
- 23
2
votes
0
answers
60
views
Uniqueness of solutions of Maxwell equations [closed]
I have this exercise on my electromagnetism course :
Consider that there exist two pairs of fields E and B that satisfy Maxwell's equations, with the same boundary conditions and have the same ...
- 21
0
votes
3
answers
489
views
What is the formula for total reactance?
Total Reactance is the sum of capacitive reactance and inductive reactance. So, it should be given by the formula
$$X = X(L) + X(C) \, ..$$
However, in some sources it is
$$X = X(L) - X(C)$$
Which one ...
user355398
0
votes
1
answer
29
views
What is the intuition for no resistance between concentric spherical surfaces if $k = 0$ in this problem? [closed]
I've currently solved problem 5.16 in Cheng's book on Field and Wave electromagnetics. The problem is stated as:
Determine the resistance between two concentric spherical surfaces of radii $R_1$ and $...
- 344
1
vote
1
answer
175
views
Feynman-Propagator of the gauge-fixed electromagnetic field
I want to find the Feynman propagator for the so called $R_\zeta$ gauge fixed electromagnetic field. The lagrangian density is given by:
\begin{align}
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\frac{1}{2\...
- 505
1
vote
0
answers
70
views
Problem 12.65 - Griffiths Electrodynamics 4.ed [closed]
I'm working on this problem from Griffiths (specifically part b), where we have to show that a current square loop (side $l$) with uniform line charge density $\lambda$, carries an electric dipole ...
1
vote
1
answer
57
views
Determine the charge distribution and the total charge of the system [closed]
Suppose we have a spherical symmetrically distributed charge in vaccuum which yields us a spherically and symmetrical potential $V(r)$ according to:
$$V(r) = V_0(1-(r/a)^2)$$
for $r\leq a$ and $0$ ...
- 344
1
vote
2
answers
298
views
Energy-Momentum-Tensor of classical electrodynamics is conserved
I want to check if the energy momentum tensor of the classical electrodynamics with lagrangian
\begin{align}
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
\end{align}
is conserved. The energy momentum tensor ...
- 505
1
vote
0
answers
30
views
Can I find the maximum magnetic flux of my magnet knowing the magnetic flux density? (and also for multiple stacked together) [closed]
I'm working on an extended essay in physics for IB with my experiment relating to the magnet down a copper tube experiment. I'm trying to find the terminal velocity with my independent variable being ...
- 11
1
vote
0
answers
118
views
Prandtl boundary layer equations for two-dimensional steady laminar flow of incompressible fluid over a semi-infinite plate are given by [closed]
Prandtl boundary layer equations for two-dimensional steady laminar flow of incompressible fluid over a semi-infinite plate are given by
jpg
- 11
0
votes
2
answers
70
views
Finding induced magnetic field due to induced current
My question is very similar to this question
So I calculated the induced electric field which in turn induces a current density in the cylinder.
But I am confused why when one divides a cylinder into ...
- 460
1
vote
0
answers
171
views
Lienard-Wiechert Potential derivation in Wald's "Advanced Classical Electromagnetism" [closed]
I want to follow the Lienard-Wiechert potential derivation in Robert Wald's E-M book, page 179. I do not understand $dX(t_\text{ret})/dt$ on the right side. I assume the chain rule is applied and $x'^...
- 139
1
vote
0
answers
72
views
Electromagnetic waves in medium with strange polarization vector
I have an exercise in Electromagnetic waves, basically to find the refractive index of a wave in a medium with polarization $\mathbf{P}=\alpha \nabla \times \mathbf{E}$. I used the Maxwell equations ...
- 147
0
votes
2
answers
86
views
Why does Faraday's law work? [closed]
A thin bar is moving parallel to a current and we want to evaluate the tension between the two extremes of the bar.
What I did was applying Faraday's law to the bar, considering the flux of the ...
1
vote
0
answers
55
views
Rewriting Maxwell Lagrangian [duplicate]
I'm having some problems with rewriting the Maxwell Lagrangian. The text states, \begin{align}\mathcal{L}&=-\dfrac{1}{4}F_{\mu\nu}F^{\mu\nu}-A_\mu J^\mu \\
&= -\dfrac{1}{2}(\partial_\mu A_\nu)^...
- 11
-1
votes
1
answer
212
views
Retarded Solutions for the Fields: Jefimenko’s Generalizations (Jackson-Electrodynamics)
On p.247 of the textbook, the author claimed we have to make some correction to move the gradient operator outside the bracket.
How does the first equation (6.53) happen?
$$
[\nabla' \rho]_{ret} = \...
- 277
-1
votes
1
answer
92
views
No limits of integration for electric field integral?
For this problem,
The solution is,
However, why have they not included limits of integration? I think this is because all the small charge elements dq across the ring add up to Q.
However, how would ...
- 49
0
votes
0
answers
24
views
How determine the angle theta if short dipole is polarized along different vectors?
i am trying to understand the solution: (i have attached q & solution key)
see part d,e,f how do we visualize rotation for gain function given different vector direction of polarization (i.e. in d,...
- 1
2
votes
1
answer
134
views
Charged particle in a purely radial magnetic field, is the canonical angular momentum conserved?
Let $ \vec{B} = k \dfrac{\vec{u_r}}{r^2}$ (assuming magnetic monopoles exist) and let $q$ be a charged particle. The associated hamiltonian is $H = \dfrac{(\vec{p} - q \vec{A})^2}{2m}$ and the ...
- 135
1
vote
1
answer
67
views
Tension generated in a metallic loop placed in a time varying magnetic field [closed]
We have a metallic wire circular loop of resistance $R$, having radius $a$, placed in a magnetic field $\bf{\vec{B}(t)}$. The magnetic field is perpendicular to the plane of the wire.
The magnetic ...
1
vote
2
answers
683
views
Finding electric field of the electromagnetic wave for given magnetic field [closed]
We are given the following information:
The magnetic field of an electromagnetic wave travelling through vacuum is given by
$$
\vec B = B_0e^{i(ky-\omega t)}\hat i + B_0e^{i(kx-\omega t)}\hat j.
$$
...
- 665
4
votes
1
answer
225
views
Is there a quick way to calculate the derivative of a quantity that uses Einstein's summation convention?
Consider $F_{\mu\nu}=\partial_{\mu}A_\nu-\partial_\nu A_\mu$, I am trying to understand how to fast calculate $$\frac{\partial(F_{\mu\nu}F^{\mu\nu})}{\partial (\partial_\alpha A_\beta)}$$
without ...
- 838
0
votes
1
answer
79
views
Potential of a Hertzian-esque dipole in Lorenz gauge
Given the current density ${\bf j}({\bf r},t) = \mathbf{v}_{0}\,\omega\, \sin(\omega\,t)\,\delta({\bf r}-{\bf r}_0),$ what is the vector potential?
From a previous question I noticed the density is ...
- 462
0
votes
2
answers
37
views
Magnetic flux due to movement [closed]
How does the magnetic flux decrease in the example shown below if the rectangle moves down due to the gravitational force, and there is no friction. The surface $A$ of the rectangle nor the magnetic ...
- 47
2
votes
1
answer
51
views
Arbitrary (Non-Radial) Charge Distribution and Gauss's Law in Integral Form [closed]
Say we have an Electric Field, produced by a charge distribution, given as-
\begin{equation}
\mathbf{E}=c(1-e^{-\alpha r}) \frac{\hat{\mathbf{r}}}{r^2},
\end{equation}
$c$ and $\alpha$ being constants....