All Questions
Tagged with electromagnetism homework-and-exercises
1,552
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What does a circularly polarized electromagnetic plane wave look like in a co-rotating reference frame?
For a circularly polarized plane wave, the $\mathbf{E}$ and $\mathbf{B}$ vectors rotate in a particular direction. For concreteness, say the electric and magnetic fields are given by:
\begin{align}
\...
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Relativistic charged particle in a constant uniform electric field
I'm doing some special relativity exercises. I have to find $x(t)$ and $v(t)$ of a charged particle left at rest in $t=0$ in an external constant uniform electric field $\vec{E}=E_{0} \hat{i}$, then ...
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Feynman propagator for arbitrary values of the gauge parameter $\zeta$
For the choice $\zeta = 1$ the Lagrangian can be brought into a particularly simple form upon integration by parts in the action integral. Equation$$\mathcal{L}' = -{1\over4}F_{\mu\nu}F^{\mu\nu} - {1\...
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Is there a better alternative to assuming $a=0$ and then calculating acceleration? (Exam question: radiated energy after Coulomb scattering)
My classmates and I are having some debate about how to solve this problem which came up on one of our comprehensive exams. A full, step-by-step solution is not needed, an outline is enough. A ...
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What is the change in flux through a loop that has been rotated?
We have a number of field lines perpendicular to one loop of wire with an area $A = 10\textrm{ cm}^2$. The magnetic field is$B= 7.2\times10^{-5}\textrm{ T}$.
You turn the loop and the flux decreases ...
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Describing a circular current loop as delta functions
It would be really nice to see how Jackson got eqn 5.33 on his example problem for finding the vector potential of a circular current loop
$$
J_{\phi}=I\sin\theta'\delta(\cos\theta')\frac{\delta(r'-a)...
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Maxwell's equations with differential form formalism
I've been reading Sean Carroll's book on GR and I stumbled upon an exercise on EM using $p$-forms. I think I've solved the problem correctly but I am having problems with my answers. I'll provide the ...
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Derivatives of Dirac delta function and equation of continuity for a single charge
For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are given by:
\begin{equation} \rho(\textbf{r},t)= e\,\delta^3(r-\textbf{R}(t))...
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Top angular speed of electric motor
I recently came across a question asking the following:
If a motor is switched on, it quickly reaches a top speed. Why does it not just go faster and faster and faster?
I thought it might be ...
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How does capacitance work?
I have a circuit whit a AC source a capacitor and a resistance all in series. I find that the difference of potential between the capacitor leads begin to change after some instants as it should. But ...
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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 ...
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What does $\mathbf{A}\cdot\nabla$ mean here?
What does $\mathbf{A}\cdot\nabla$ mean in an expression like $(\mathbf{A}\cdot\nabla)\mathbf B$?
I found this in Griffiths’ Classical Electrodynamics book and cannot figure it out.
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Does a homogeneous oscillating electric field produce a magnetic field?
I am working on a homework problem that says an electron in a continuous laser field can be modeled as experiencing a homogeneous oscillating electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}...
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Electric field on a spherical shell with a disk cut out
I came across this problem in Electricity and Magnetism by E.M. Purcell:
A spherical shell of radius $a$ is charged with a uniform surface charge density $\sigma$. A small hole of radius $b <<...
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