All Questions
Tagged with electromagnetism homework-and-exercises
257
questions with no upvoted or accepted answers
4
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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
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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
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350
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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
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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
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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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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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336
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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
100
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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
133
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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
2
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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}\...
- 1,665
2
votes
1
answer
130
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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, ...
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