All Questions
Tagged with electromagnetism homework-and-exercises
1,552
questions
11
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1
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Question about superconductivity
A long cylinder of radius $R$ is made from two different material. Its radius $r<r_0$
$(r_0<R)$ part is a material with superconducting transition temperature $T_1$, and its $r_0<r<R$ ...
- 1,191
10
votes
5
answers
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Why does a ring falling through a magnetic field experience an upward force?
The Problem states:
A metallic ring of Mass $M$ and radius $r$ falls freely under the influence of gravity in the direction along the negative Z-axis. A magnetic field $B_z = B_0(1-z\lambda)$ where ...
- 127
9
votes
5
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Is gravity non-negligible compared to the electromagnetic force?
Consider two electrons approaching each other at rather fast speeds, maybe even coming close to colliding. Does gravity play any role in this event? If so, how much influence does it have? Do we need ...
9
votes
4
answers
668
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Distribution of point charges on a line of finite length
How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
- 4,194
9
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Electron in the proximity of a magnetic monopole
I am puzzling about an exercise in the book "Electromagnetic Theory" by Ferraro (p.543).
An electron (mass $m$, charge $-e$) in a monopole magnetic field $\vec{B}\left(\vec{r}\right)=g\frac{\vec{r}}{...
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9
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2
answers
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Why does the dimension of the electric charge depend on the number of spacetime dimensions?
We can find via dimensional analysis that the dimension of the electric charge varies with the dimension of space-time $(D+1)$:
$$[\text{charge}] = (\text{eV})^{(3-D)/2}.$$
It is dimensionless if ...
- 944
8
votes
3
answers
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Derivation of the speed of light using the integral forms of Maxwell's Equations
Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
- 905
8
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1
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The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\...
- 81
8
votes
1
answer
406
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Quantum Cyclotron Frequency - Why is it off by a factor of 2?
Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is:
$$H = \frac{1}{2m}[\vec{p}-e\vec{A}]^2-\vec{\...
- 1,212
7
votes
2
answers
784
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Approximating an expression for a potential
In a problem which I was doing, I came across an expression for the potential $V$ of a system as follows $$V = k\left(\frac{1}{l - x} + \frac{1}{l + x}\right)\tag{1}\label{1}$$ where $k$ is a constant,...
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7
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1
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How much power would it take to stop a bullet with a magnet?
If a 7.5 gram copper-jacketed lead bullet (say, a 9x19mm Parabellum) was travelling at 360 m/s, how much power would it take to diamagnetically stop it in the space of one meter?
This question comes ...
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7
votes
2
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Derivation of the quadratic form of the Dirac equation
I am asked to derive the quadratic form of the Dirac equation in an electromagnetic field,
$\left[\left(i\hbar \partial - \frac{e}{c}A\right)^2 - \frac{\hbar e}{2c} \sigma^{\mu\nu} F_{\mu\nu} - m^2c^...
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7
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5
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Hollow conductor containing charge: why is internal field cancelled outside and why are the field oustide the cavity zero inside the cavity?
I've a doubt on the following situation. Consider a hollow conductor $A$ (of arbitrary shape) containing another conductor $B$ (again of arbitrary shape), with a positive charge $+q$.
By the ...
- 2,617
7
votes
1
answer
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Homopolar motor and Lorentz force
My second grader thought making a homopolar motor for her science experiment would be fun. And, it was. Now I am trying to explain how it works and the Lorentz force. Please help me by giving me a ...
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7
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1
answer
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Magnetic field from a half-cylinder [closed]
I am preparing for an exam, on this problem I had the opposite direction of the magnetic field.
A conductor-cylinder with radius R has been cut in half ($\phi \in [0,\pi]$)
A DC current $I$ runs ...
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