All Questions
45
questions
2
votes
3
answers
204
views
Deriving continuity equation from 4-current of a charged particle
how can i check that following 4-current for a single charged particle
$$j^{\mu}(x)=qc\int d\tau u^{\mu}(\tau)\delta^{4}(x-r(\tau))$$
satisfies continuity equation $$\partial_\mu j^\mu = 0.$$
user391340
0
votes
0
answers
29
views
Non-standard circuit
I partially solved this problem.
Problem: A charged sphere of radius $a$ is connected through a resistance $R$ to the earth. An electronic flow breaks out towards the sphere of infinity at speed $v$ ...
1
vote
1
answer
57
views
Determine the charge distribution and the total charge of the system [closed]
Suppose we have a spherical symmetrically distributed charge in vaccuum which yields us a spherically and symmetrical potential $V(r)$ according to:
$$V(r) = V_0(1-(r/a)^2)$$
for $r\leq a$ and $0$ ...
- 344
0
votes
1
answer
78
views
Potential of a Hertzian-esque dipole in Lorenz gauge
Given the current density ${\bf j}({\bf r},t) = \mathbf{v}_{0}\,\omega\, \sin(\omega\,t)\,\delta({\bf r}-{\bf r}_0),$ what is the vector potential?
From a previous question I noticed the density is ...
- 462
2
votes
1
answer
51
views
Arbitrary (Non-Radial) Charge Distribution and Gauss's Law in Integral Form [closed]
Say we have an Electric Field, produced by a charge distribution, given as-
\begin{equation}
\mathbf{E}=c(1-e^{-\alpha r}) \frac{\hat{\mathbf{r}}}{r^2},
\end{equation}
$c$ and $\alpha$ being constants....
0
votes
2
answers
342
views
Maxwell Equations Solution for single charged particle
Is it possible to find an analytic solution to maxwell equation when I have only one charged particle (and without any neglections):
With $\rho=q\delta(r-r_a)$, $J=q\dot{\vec{r_a}}\delta(r-r_a)$ and $...
- 1,734
0
votes
1
answer
28
views
What is the distribution of surface charge of the inner conductor of this system? [closed]
Given the following system, where the conductors (marked as yellow in the picture) have spherical symmetry. The inner conductor has $\textit{+Q}$ charge and the outer conductor has $\textit{-Q}$ ...
- 177
0
votes
1
answer
192
views
Initial charge in parallel plate capacitor [closed]
Two capacitors $C_1$ and $C_2$ (where $C_1 > C_2$) are charged to the same initial potential difference $\Delta V_i$. The charged capacitors are removed from the battery, and their plates are ...
- 125
-3
votes
1
answer
81
views
Centre of Circular Motion of $q$ in a Uniform Magnetic field [closed]
Initial Conditions
A charged particle $q$, is initially at rest at $(x,y)$. It is given velocity, $v_o~m.s^{-1}$ along positive $X$-axis.
There exists a Uniform Magnetic Field $B_0$ in the whole ...
- 218
0
votes
0
answers
77
views
Find the electric field from a distance of a positively charged metal sheet
A square metal sheet with area $2\,\mathrm{m^2}$ and thickness $10\,\mathrm{mm}$ has gained a positive charge of $10\,\mathrm{pC}$. Find an the electric field $15$ meters above the metal sheet.
I don'...
- 67
-1
votes
1
answer
38
views
Eletrical Field created by a charge surface on a point [closed]
I was answering this question and even tho i know intuitively that the radial component of the eletric field will cancel out by simmetry, i could not get that in the integral calculation. I´m asking ...
0
votes
1
answer
197
views
Getting the current density of a wire with given surface charge density [closed]
I found this question, which seemed very easy to me at first, but when I revisited the problem I started to have some doubts about my approach, so I would appreciate any form of discussion or approval ...
- 53
1
vote
0
answers
16
views
When do travelling (accelerating) charged particles emit radiation in their direction of travel and when perpendicular to their velocity? [closed]
I have read numerous things saying that a travelling charged particle emits radiation primarily in a cone in the direction of travel, and other places say the radiation is emitted and polarized in an ...
- 4,515
1
vote
2
answers
139
views
Motion of Test Charge in EM Field [closed]
I have a negative infinite sheet of charge moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ with mass $m$ moves at a constant velocity $v$.
My Question is simple: How will the test ...
- 313
0
votes
1
answer
61
views
How do I find the radius of motion of this particle? [closed]
A charged particle $Q$ centers a region of uniform magnetic field $\vec B=B\hat x$ at the origin, moving in the positive $z$-direction. It follows a circular arc of less than $\frac{\pi}{2}$ and is ...
- 1