All Questions
Tagged with electromagnetism homework-and-exercises
258
questions with no upvoted or accepted answers
4
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answers
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views
Purcell/Morin: Why is approximating the resistance of a tapered rod using disk slices in series not adequate when the taper occurs very quickly?
The following exposition and question are based on two problems from the book "Electricity and Magnetism" by Purcell and Morin (problems 4.32 and 4.6 from Chapter 4 called "Electric ...
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4
votes
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answers
1k
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Landau quantization: degeneracy of first level
In some books the degeneracy of one Landau level in a two-dimensional gas of free electrons is calculated in the following way:
Note: The electron spin is not considered.
Number of states of a free ...
- 171
4
votes
3
answers
351
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Magnetostatics or dynamics?
A spherical conductor, carrying a total charge $Q$, spins uniformly and very rapidly about an axis coinciding with one of its diameters. In the diagrams given below, the equilibrium charge density on ...
- 1,389
3
votes
1
answer
155
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Non-linearities in Lagrangian of a scalar field coupled to point-like source
I have an exercise where I did not manage to understand the questions. Basically, I have this Lagrangian
\begin{equation}
\mathcal{L}=\frac{1}{2}(\partial \pi)^2-\frac{1}{\Lambda^3}(\partial \pi)^2\...
3
votes
0
answers
629
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Poynting theorem on an example?
I understand the basic statement of Poynting theorem of conservation of energy relative to electromagnetic field.
However, I fail to apply it to an example.
Consider this classical case:
...
- 1,110
3
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174
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Question about the fields in a solenoid
I am very familiar with using Ampere's Law to find the B field inside a solenoid ($\mu_0nI(t)$). Then I can use Faradays to find the E field inside ($\propto\dot I$).
I want to get this result ...
- 1,788
3
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88
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Charge distribution and potential in a 1-dimensional quasistatic system
Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(...
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3
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378
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Angular momentum of particle in dipole magnetic field
Basically I'm just trying to find the expression for the angular momentum of a particle of mass $m$ and charge $q$ in a dipole magnetic field. In cylindrical coordinates, $\vec{v}=v_{\rho}\hat{\rho}+...
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339
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Bandgap Spacing in Photonic Crystals
I am doing some self-study on photonics and have encountered the following question:
We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
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3
votes
1
answer
1k
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Distribution of current of a rotating cone
If I have a hollow cone (surface with no bottom cover ) as the one in the picture. The cone has surface charged density $\sigma$. It rotates around the symmetry axis with an angular velocity $\omega$. ...
- 738
2
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57
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Charged pendulum and a fixed point charge
!My set-up is the following: i have an iron bolt suspended on a string next to an electromagnet, of which I steadily increase the voltage and thereby the magnetic field. Supposing the force is linear ...
- 21
2
votes
1
answer
101
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Primary constraint of electrodynamics
I have some problems understanding the transition from the Lagrangian to Hamiltonian formalism of electrodynamics. I will use the metric $(-+++)$.
I want to start from the Lagrangian which is ...
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 ...
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2
votes
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answers
111
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How do I calculate the functional derivative of the EM action on the curved spacetime with respect to the metric?
I am having trouble with computing the functional derivative with respect to the metric of the EM on a curved spacetime:
\begin{equation}
S:=\frac{1}{16\pi^2 G}\int R \sqrt{-g}\text{ }d^4x-\frac{1}{4}\...
- 1,669
2
votes
1
answer
131
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Fermion number non-conservation in parallel $E$ and $B$ fields
This is from Problem 19.1 in Peskin and Schroeder.
(a) Show that the Adler-Bell-Jackiw anomaly equation leads to the following law for global fermion number conservation: If $N_R$ and $N_L$ are, ...
- 409
2
votes
1
answer
58
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Manipulation of the diffusive term in MHD induction equation
I am trying to solve the magnetohydrodynamic (MHD) equations with a spatially varying resistivity, $\eta$. To remove some of the numerical stiffness from my finite volume approach, I am trying to get ...
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2
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154
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Debye length for a debye shield
I understand debye length and even the concept of debye shielding, but quantitatively I'm a little confused. If the debye shield has a potential of $$\Phi=\frac{q}{4\pi\epsilon_{0}r}\exp\left({\frac{-...
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2
votes
1
answer
51
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Questions on Forces involved in oscillating mass dipole
Say we have two balls of radius $R$ on both sides of a massless dielectric rod and it starts oscillating due to an external electric field. Other than the external field would there be an electric ...
2
votes
0
answers
118
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Magnetic field due to a double tape line
I have been asked to calculate the inductance of a double tape line :
Now we know that $$ N\phi = LI$$
So let's calculate the magnetic field by assuming an amperian loop like this:
$$\int B.dl = ...
- 361
2
votes
0
answers
406
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Derivation of Coulomb's law from classical field theory
In the section on Coulomb's law in QFT by Schwartz, he expands $-\frac{1}{4}F_{\mu\nu}^{2}$ to get $-\frac{1}{2}(\partial_{\mu}A_{\nu})^{2} + \frac{1}{2}(\partial_{\mu}A_{\mu})^{2}$, can someone ...
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132
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Input impedance of a line with complex load
I am currently studying electromagnetism mostly with the help of the book "Microwave Engineering" and when trying to solve problems which main goal is to compute the input impedance of a lossless ...
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2
votes
1
answer
69
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Faraday Tensor quadruple product
I would like to compute the following:
$$F^{ab}F_{ac}F_{bd}F^{cd}$$
Is this equal to $4(E^2-B^2)^2?$
If so how can i quickly calculate it as such?
- 1,488
2
votes
1
answer
145
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How to prove this matrix differential for Born-Infeld theory?
Consider the Born-Infeld Lagrangian, page 30 of Born-Infeld Action and Its
Applications by Cong Wang.
$L_{BI} = \sqrt{\det (1+ F)}$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. I ...
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3
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823
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Why does voltage cancel out if a circuit is going through a magnetic field?
The answer says that there is no current as there is no voltage, but why is there no voltage even though they cut field lines?
EDIT; I found the answers, but still not really understanding it
- 157
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0
answers
102
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Possible Magnets
Okay so I was going through my book and found this interesting question --
Which of the following is possible?
$a)$ a magnet with no poles
$b)$ a magnet with two poles
$c)$ a temporary magnet ...
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2
votes
0
answers
154
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One from Landau's Minimum (Macroscopic Electrodynamics)
A dielectric
sphere with the electric and magnetic susceptibilities ε1 and µ1 is rotating with
angular frequency ω in a constant electric field E~ in a medium, characterized
by the parameters ε2 and ...
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2
votes
0
answers
208
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Second-order correction in Quantum-Confined Stark effect
In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
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2
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492
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Motion of a charged particle in a "solid" charged sphere (accounting for radiation)
Consider a particle (point charge) with charge $q$ and mass $m$ that crosses into a uniformly charged sphere (with charge $Q$ and radius $R$). The trajectory of the particle is a diameter of the ...
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480
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Magnetic flux density a small distance off axis from a current loop
I'm currently studying physics at University and struggling with the problem mentioned, it's on a past paper I'm trying to do.
I have calculated the B field on axis as (sorry don't know how to format ...
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