I am currently a sophomore in HS, and I have a science fair project next year. I want to do something interesting- I don't want to put in barely any effort and do something that everyone has done, like 'growing plants in different light levels'.
I would ideally like to do something with...
The electric field inside a charged spherical shell moving inertially is, per Gauss's law, zero.
If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.
The...
Hi.
I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up.
(Edit- I can solve this problem in the...
This was a trivial question I had (which I posted here on the PF EM Forum: https://www.physicsforums.com/threads/bound-charges-polarisation-of-a-half-cone.1015308/).
As I received no response on the above link I decided to post the same as a self formulated HW problem. Below I have attached an...
Summary:: There seems to be a mismatch, in the "Maxwell's" equations, between the number of equations and number of variables.
I was trying to play around with the equations for Electromagnetism and noticed something unusual. When expanded, there are 8 equations, 6 unknown variables, and 4...
In Purcell's E&M Section5.3 "Measurement of charge in motion", he said when a charge is in motion, the force on test charges may not be in the direction of radius vector r. And in next paragraph, he defined Q by averaging over all directions.
However, he just measured the radial component of...
In a problem of an oscillating electric dipole, under appropriate conditions, one can find, for the potential vector calculated at the point ##\vec{r}##, the expression ##\vec{A}=\hat{k}\frac{\mu_0I_0d}{4\pi}\frac{cos(\omega(t-r/c))}{r}## where: ##\hat{k}## is the direction of the ##z-axis##...
While reading about electromagnetism from the OpenStax books with my son (and doing some experiments), he asked this question.
Suppose I hang a pendulum and make it oscillate inside a coil connected to a Galvanometer as shown in the schematic diagram:
Hopefully the image is clear enough. His...
I'm preparing for exam but it seems I can't find problems similar to this on the internet.
Here I will apply Gauss's law on the electric field vector to get the charge density. but the problem is that I can't find similar examples on the internet that uses direct vectors on Maxwell's equations...
The electromagnetic field can carry waves, some of them are light, others are used in radio broadcast. These oscillatory waves are distinguished by their frequency. The usual pickup that we get from electric currents in the circuits in the walls of the building has a frequency of about 100...
I want to show that the action staying the same action after taking ##A^\mu \to A^\mu + \partial ^\mu \chi##, for the first term I suceeded in showing the invariance using the fact ##[\partial ^ \mu , \partial ^\nu]=0## but for the second term I'm getting: ##\epsilon^{\alpha\mu\nu}A_\alpha...
Hi, everyone. I just finished studying the principle on which a transformer works. It relies on Faraday's law of induction. And my high school physics book uses the following picture for illustration:
Roughly speaking, the...
I am reading Griffith's textbook on EM. There is a problem asking to find the force acting on the northern hemisphere by the southern hemisphere of a uniformly charged sphere.
The solution idea is to find the expression of the E field by Gauss's law and integrate the force over the northern...
So my idea was that to reach the equilibrium position, the final moment of force has to be 0 (so in the end the forces will “eliminate” each other). And I found the equation Fm=B*I*l*sinα, which should characterize the force, which affects wire with the current in a magnetic field, and Fleming’s...
The experiment consists of a large field coil (connected to a current source) surrounding a coplanar and coaxial small detector coil in the center of the field coil connected to the oscilloscope.
1. Matching Current v. Time Graphs to Oscilloscope Graphs
Example of one pair of graphs (I'll...
Summary:: Can anyone introduce an informative resource with solved examples for learning variation principle?
For example I cannot do the variation for the electromagnetic lagrangian when ##A_\mu J^\mu## added to the free lagrangian and also some other terms which are possible:
$$
L =...
Mary Boas attempts to explain this by pointing out that the situation cannot arise because charges will have to be placed individually, and in an order, and that order would represent the order we sum in. That at any point the unplaced infinite charges would form an infinite divergent series...
At first I take the uniformly distributed charge and then divide it by the area of the carpet to get the surface charge density σ
-10E-6 C / 8m^2 = σ = -1.25E-6C/m^2
Then I divide the surface charge density by 2e0 to get the electric field strength caused by the infinite plane...
The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by
$$\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...