All Questions
45
questions
2
votes
3
answers
206
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
79
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
347
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
193
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 ...
- 4,509
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
0
votes
2
answers
99
views
Lorentz Force and Circular motion - What is the magnetic field causing the movement? [closed]
I am given this problem:
A particle with mass $m$ and positive charge $q$ is moving in the following path on the $x$-$y$ plane. It's path consists of semicircles as shown below. The particle's ...
2
votes
1
answer
75
views
Two protons inside a negative sphere [closed]
Problem: Imagine a sphere of radius a filled with a negative charge density equal of two electron charge.
Embedded in this is two protons, assume that the negative charge distribution remains uniform
...
- 123
0
votes
2
answers
228
views
Null electric field at infinity? How? [closed]
Suppose there are two charges (4uC each) fixed in the horizontal axis. One is in x=0 and the other in x=8m.
I've obtained the electric field:
$E=-k\cdot4\mu C \cdot [\frac{1}{x^2}+\frac{1}{(x-8m)^2}]...
0
votes
3
answers
266
views
If the speed of electron (in space) is increased, will the magnitude of current also increase? [closed]
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
(a) The ...
- 107
2
votes
0
answers
878
views
Does a rotating disk with uniformly distributed charges have energy radiation? [closed]
Problem:
A disk of radius 10 cm is injected with an amount of charge of 3×10^−12 C, uniformly distributed along the edge of the disk. The disk rotates with an angular velocity of 10 rad/s. Find the ...
- 21
0
votes
1
answer
174
views
Motion of an electron near a proton [closed]
Statement of the problem:
Consider an electron and a proton that are initially at rest separated $a$ meters. Do not take into account the movement of the proton, because its mass is much greater ...
- 163
0
votes
1
answer
57
views
Charged particle in uniform $\vec{B}$ and $\vec{E}$ [closed]
A particle of mass $10^{-26}\ kg$ and charge $1.6\times 10^{-19}\ C$ traveling with a velocity of $1.28\times 10^{6}\ m/s$ in the $+x$ direction enter a region in which a uniform electric field $E$ ...
- 253
1
vote
2
answers
2k
views
Does a permanent magnet attract a positively charged rod?
I thought that because the charge on the rod is static, there wouldn't be an interaction with the magnetic field, however the answer to the question states that both poles of the magnet would attract ...
- 38
0
votes
1
answer
396
views
The charge density $\rho_{\infty}$ of the sphere
I have two charged hemispheres (which are very close to each other, we
consider them now as a sphere) with the charge density given as $\rho
= \frac {Q}{\pi a^3 \frac {4}{3+n}} (\frac{r}{a})^n$, ...
user156350
1
vote
0
answers
102
views
Parametric equation for a weird trajectory in affect of gravity and magnetic field [closed]
This is a question from Bangladesh Physics Olympiad:
Draw the trajectory of the charge $+q$ .Necessary informations are given in the figure. $B$ is the magnetic
field.
What I want to know is ...
- 1,228
0
votes
2
answers
287
views
One dimensional inverse square law - motion of charged particles
I'm working on a simple case of two oppositely charged, equal-mass particles in a 1-dimensional system. It might as well be an electron and positron, but without the case of annihilation on contact. ...
- 1
3
votes
2
answers
875
views
Electric field outside wire with stationary current
Consider a conductor of arbitrary structure where a stationary current flow, that is
$$\nabla \cdot \vec{j}=0$$
I did not find on textbook clear explanations on two facts:
How is the electric ...
- 2,617
1
vote
2
answers
1k
views
How can I keep a charged particle between two capacitor plates?
To make this practical, let's make a problem out of it. And our problem would be explained as follows:
We have a small sphere that weighs x kg and is placed inbetween two parallell plates in an air-...
- 13
1
vote
2
answers
2k
views
Charged body in hollow conductor : what is the role of insulators and how does the charge distribution change if insulators vs conductors are used?
Question as written in textbook: "Figure 1 illustrates a nested arrangement of four cylindrical conductors (seen side-on in cross-section) in which the cylinders are separated by electrical insulators....
- 1,367
1
vote
2
answers
1k
views
Zero electric field in empty region of hollow conductor
A hollow conducting shell having a net charge of +Q has a point charge -Q placed at its centre.
From the diagram, it looks like
Suppose the radius of the inner shell from the origin is a and the ...
- 889
0
votes
1
answer
209
views
Force from a large conducting plate [closed]
How can I find the distance to a test-charge, hoovering below a conducting plate? Newtons laws applies.
$$
$$
According to this information, I conclude that the force is equal zero. It is not moving....
- 31
-3
votes
2
answers
7k
views
How to determine the angular velocity of a particle with mass $m$ and charge $q$ in a constant B field? [closed]
$\textbf{PROBLEM:}$
A particle with mass $m$ and charge $q$ moves in a constant magnetic field $B$. Show that, if the initial velocity is perpendicular to $B$, the path is circular and the angular ...
1
vote
1
answer
337
views
Why can't I measure electric potential from source to point according to this formula
The formula for electric potential of points A and B in the presence of an electric field due to a point charge where $R_a$ and $R_b$ are the distances from source to point A and B respectively is:
$${...
- 163
0
votes
1
answer
460
views
How do I determine the electric charge on two (initially discharged) spheres after an impact with a charged sphere?
This is the first part of a problem on my book:
Two identical conducting spheres, initially discharged, of mass $ m = 0.5 \ kg $ come in contact, in consecutive moments, with another sphere, ...
1
vote
1
answer
48
views
a charged particle path [closed]
A particle of mass $m$ and charge $e$ enters a homogeneous and stationary electric field $E$ with velocity $v_0$ perpendicular to the direction of the field.
Calculate the particle's path?
What does ...
- 145
0
votes
1
answer
3k
views
Using Cosine Law to Find Net Electric Force on Charge Always Results in Positive Number?
In order to determine the net force other charges have on a particular charge, you must take into account each individual electric force between the charge and the charge of interest. However some of ...
- 21
1
vote
2
answers
423
views
Description of the motion of the COM of a system of charged particles moving in a magnetic field
I recently came across a problem where an electrically neutral particle is at rest in a uniform magnetic field. The particle now splits into two charged particles of equal mass $m$; charge and mass ...
- 2,077
0
votes
1
answer
908
views
Question regarding 2 conducting spheres connected by a long fine line (electric potentional)
I'm having a bit of trouble understanding a pretty simple issue.
Assuming I have 2 conducting spheres uniformly charged connected by a long fine line (as shows in the added photo) and im being asked ...
- 137
0
votes
1
answer
135
views
How does this particle behave in the magnetic field?
I have the above question and I have though about it every way and can't seem to find out. So what I have concluded (ignore the answers on the img) Is that the force is on the z axis because the cross ...
- 23
1
vote
0
answers
2k
views
Electric potential on a uniformly charged tube
A hollow cylinder, with no top or bottom, of radius $R$ and length $L$ is uniformly charged with density $\sigma>0$. I have to find the point on space where a point charge $q>0$ has to be drawn ...
- 31
0
votes
1
answer
2k
views
Electric potential difference from electric field of isolated spherical conductor
I'm wondering if my train of thought is correct. Say you have Point $A$ which is $A$ distance away from the center of an isolated spherical conductor, and Point $B$ which is $B$ distance away from the ...
- 149
-6
votes
1
answer
6k
views
Are dc and ac currents produce electric field? [closed]
I have four different situation and i want to learn what kind of field (electric or magnetic) each produces and which produces electomagnetic waves?
1)dc current flow in a conductor
2)ac current ...
- 25
9
votes
4
answers
668
views
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
13
votes
1
answer
560
views
How can I find the position of an image charge when the boundary is parabolic or hyperbolic?
If the position of some charge $Q$ is known, the boundary condition is $u=0$ on some parabolic surface, and we know the image charge has its electric volume of $Q'$, then how can I determine the ...
- 147
3
votes
1
answer
1k
views
Electric Field due to a charged sphere
Suppose we have a spherical surface with a surface charge density varying as $cos(\theta)$. Apparently one can find the electric field both outside and inside such a spherical surface by superposing ...
- 33