All Questions
Tagged with electromagnetism homework-and-exercises
258
questions with no upvoted or accepted answers
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How does Schwinger transform a static $(\phi,0)$ to $(\phi ', A)$ in a moving frame?
Schwinger writes in his paper Electromagnetic mass revisited:
Any spherically symmetrical charge distribution of total charge $e$, at rest, is represented by the potentials
$$\phi \sim ef(r^2),...
- 3,108
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Abstract approach to the total electric force on a charged rod
Suppose we have a 1-dimensional system (x-axis) consisting of rod of finite length $l$ and arbitrary charge density of $\lambda(x)$ at rest extending from the origin to $x=l$. And now, suppose we have ...
- 165
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How to calculate pole strength for this magnet?
I know magnetic mono poles don't exists and a magnetic poles always have equal strength. But what about a magnet which looks like this?
This is picture of magnet whose thickness is constantly ...
- 1,691
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MCS Lagrangian and Euler-Lagrange
I'm trying to solve the Euler-Lagrange equation for the MCS Lagrangian density as given by Kharzeev in this article (Eqn. 7):
$$ \mathcal{L}_{\textrm{MCS}} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^{\...
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Energy of static magnetic field
I learned that the energy density of the magnetic field is
$$\mathcal{E}=\frac{1}{2\mu_0}\mathbf{B}\cdot\mathbf{B}$$
This can be derived by analyzing the Maxwell equation and from the procedure ...
- 962
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Electromagnetic wave in a prism
Imagine an electromagnetic plane wave entering perpendicular to one of the faces of a prism with the form of a triangle rectangle, which is made of a certain material of refraction index $n$. The wave ...
- 1,172
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Magnetic field $\vec{A}$ as momentum potential
I was reviewing some topics on electromagnetic field theory and I came across the following interesting assertion: the electromagnetic moment $P_{EM}$, which is defined in vacuum as:
$$P_{EM}=\frac{1}...
- 1,172
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Does the electrodynamics-like PDE $\epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$ have solutions?
Consider the following PDE in 3 dimensions
$$ \epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$$
Does $B_{kl}(x)$ have a solution? (It can have any kind of singularity, e.g. it can have ...
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Does the absorption intensity for vibrational transition depends on the angle between the electric field vector and the transition moment vector?
Is the transition possible even if there is a certain angle between the electric field vector and the transition moment, given that the photon and molecule are in resonance. My notion is that the ...
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How to calculate the magnetic field of two cylinders when one of them is rotating
Given is the voltage U and the Angular velocity $\omega$. The rotating cylinder is inside the other cylinder and U is measured between them.
To calculate the magnetic field, I tried to solve
$\oint ...
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527
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Particle in electromagnetic field Lagrangian
Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
- 141
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74
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Magnetism: EMF induced by a conducting balloon filling with water
Info:
As stated in the title, I'm wondering how to find the EMF induced by a conducting balloon. This balloon is under a waterfall, and it expands and contracts as water is filled in it, with a flow ...
- 11
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299
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the general solution of the motion in the xy-plane of cyclotron for given E and B
A particle of charge e and mass m moves in a region of uniform electric field E directed along Ox and a uniform magnetic field B directed along Oz.
Show that one solution (called a particular integral)...
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Non-radiation charge density
For all $l,m$ but $l=0,m=0$, can we find $r_0,w_0$ such that the following charge distributions can represent a charge field that does not radiate:
$$
\rho(r,\theta,\phi) = \Re(c_{l,m} Y_{l,m}(\theta,...
- 371
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What characteristic length should I use to calculate the magnetic Reynolds number?
I am trying to find the braking torque in an eddy current braking system for the setup shown below. I want to consider skin effect for high speed applications. My approach so far has been as follows:
...
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