The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by
$$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$
Faraday's law of induction for the induced EMF ##V_c## in a coil...
Summary:: Suggest a geometry
Hello! I have difficulties with this question. It is translated from Swedish so if something's weird tell me.
The speakers in headphones often work with the help of magnetism, when a varying voltage is applied across a coil attached to the speaker membrane. The...
If so, what will I measure in the Ampermeter, the zero total current or the value of the conduction current?
I was thinking of the following example- a circuit consist of a current source, an Ampermeter, a switch, and a semiconductor. The semiconductor can have both conduction and displacement...
Purcell says that taking the surface integral of the magnetic field ##\textbf{B}## over the surfaces ##S_{1}, S_{2}, S_{3},...## below is a good way of finding the average of the volume integral of ##\textbf{B}## in the neighborhood of these surfaces.
More specifically, he says in page...
Can anyone please tell me why the torque on a circular current loop can be calculated by the equation below? In other words, what is the intuition for the formula? Thank you. (I modified my question to a particular case)
$$ \vec{\tau} = I \vec{A} \times \vec{B} $$
In my latest 10th grade physics lesson, we were learning about the refraction of light. I decided to share what I knew about why light slows down in a vacuum, which is, in short, because the electric field of the electromagnetic wave exerts a force on the charged electrons of a medium, which in...
Let r = position of the electron = 6mm - 36.8μm; λ = mean free path traversed.
Integrate E(r) = Q/(2πϵLr) between the two shells gives:
V = [Q/(2πϵL)]*log(r/(r-λ))
I know that the question is asking for the voltage at which the electron energy will get to 23eV, but i am unsure how to get rid...
I am required to find the direction of the electric field on the surface of a grounded conducting sphere in the proximity of a point charge ##+q##. The distance between the center of the sphere and the point charge is ##d## and using the method of images we find that the charge of the sphere is...
I need some rigorous introductory books on Electromagnetism, by rigorous I mean detailed and mathematical.
Many books that I have found don’t actually work out the field produced by current carrying toroid, solenoid or even some other simple electrostatic situations. They just write “by...
Summary:: I need to add references for several classical electromagnetism concepts, I would like to know which books deal with these concepts.
Recently a paper about classical electromagnetism that I had submitted was rejected, among other reasons because it contained many references to...
Hello!
In Optical fibers, let ##k_1## and ##k_2## be respectively the propagation constants in core and cladding, ##\beta## the propagation costant of a mode along the direction ##z##, ##a## the radius of the fiber. Using the normalized quantities ##u=a \sqrt{k_1^2 − \beta^2}## and ##w=a...
When we calculate the curl of magnetic field, that is the curl of Biot-Savart equation for magnetic field. Please consider these .
The working of last equation $$ \nabla \times \mathbf {B} = \frac...
I am trying to answer exercise 5 but I am not sure I understand what the hint is implying, differentiate with respect to ##p_\alpha## and ##p_\beta##, I have done this but nothing is clicking. Also, what is the relevance of the hint "the constraint ##p^\alpha p_\alpha = m^2c^2## can be ignored...
There was an old thread comparing the difficulty of classical mechanics and electromagnetism. The consensus was that electromagnetism is more difficult, and substantially so according to some. The thread was no longer open for replies, but it got me suspecting that we're comparing apples to...
Since it is stated that ##E'_x = E_x##, I am going to set a special case where ##z' = z = 0##, ##E_x## in (5.10) reduces to,
##E_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{x^2}##
However, ##E'_x## in (5.13) reduces to,
##E'_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{\gamma^2 x'^2}##
There is an...
I am having problem with part (b) finding the vector potential. More specifically when writing out the volume integral,
$$A = \frac{\mu_0}{4\pi r}\frac{dq}{dt}\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{?}\frac{1}{4\pi r'^2} r'^2sin\theta dr'd\theta d\phi$$
How do I integrate ##r'##?
The solution...
A square conducting loop of side length a is in a non-uniform magnetic field. The loop occupies the first quadrant of the xy plane, i.e. the space between the origin (x, y) = (0,0) and the point (x,y) = (a, a). The magnetic field is in the +z direction. Develop an expression for the magnitude of...
While writing out the Dyson series due to the time ordering above I encountered the two expressions
$$T(\mathcal{L}_{int}(x))\quad \text{and}\quad T(\mathcal{L}_{int}(x)\mathcal{L}_{int}(y))$$
I was able to write out the first term in terms of contractions using Wick's theorem and then finally...
I was reading that in inverse scattering approach, we divide the region of interest into discrete grids and size of each grid should be much smaller than the incident wavelength (usually smaller than one-tenth of wavelength).
By this logic, theoretically, I can use inverse electromagnetic...
Can someone provide me intuitive visualization of how E or H field can be longitudinal in a waveguide (TM/TE)? TEM is easy to visualize, but how EM wave can behave like sound in a waveguide (constant phase and amplitude plane in the same direction)?
[Moderator: large bold font removed. In the...
This question is motivated by Problem 7.12 in Griffiths Electrodynamics book. I have not included it in the homework section, because I have already solved it correctly. However, I question whether my solution which agrees with the solution's manual is correct.
Relevant Equations:
$$\Phi =...
For reference, this is from Griffiths, introduction to quantum mechanics electrodynamics, p253-255
When deriving the ideal magnetic dipole field strength, if we put the moment m at origin and make it parallel to the z-axis,
the book went from the vector potential A
$$
A=...
Does anyone know the answers to this, or can hopefully guide me to a text that will help me solve this aharonov-bohm problem?
Here is the given:
Particles (of mass m, and charge q), are driven through two slits that have distance d between them, in a screen that is far away (L>>d) from the...
Hi everyone,
I'm pretty new to electromagnetism and have no experiences in this topic.
I have a signal generator (Digital Dual Channel Funktion Signal Generator) and want to generate two signals (530 and 550 Khz signal) and want to transmit these generated signals to the points on a table...
I know the current of capacitor and inductor must be parallel but pointing in opposite direction due to the fact they are connected in parallel thus having same voltage (please see attached screenshots). The current of resistor will simply be the sum of these two vectors, but what about its...
Under Newton, gravity is what I term an "invisible magic rope" that pulls you down.
Enter Einstein. We do away with the invisible magic rope, and say that space (or space-time) is warped by mass.
However, we still have other forces, that (as far as I know, anyway) are "invisible magic ropes."...
While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations ##(23\ a)## and ##(23\ c)## in the article (avoiding the surface integral):
##\displaystyle \psi_m (\mathbf{r})=-\dfrac{1}{4 \pi} \int_V...