Electromagnetism Definition and 830 Threads

Imagine that two charged particles, with charge ##+q##, start at the origin and then move apart symmetrically on the ##+y## and ##-y## axes due to their electrostatic repulsion. The ##y##-component of the retarded Liénard-Wiechert vector potential at a point along the ##x##-axis due to the two...

I’ve heard that in some countries (for example, Argentina), the curriculum is structured differently from the typical American program. In the U.S., students usually take a general physics course first, then move on to a textbook like Griffiths, and only encounter Jackson at the graduate level...

I am currently undertaking a research internship where I am modelling the heating of silicon wafers with a 515 nm femtosecond laser. In order to increase the absorption of the laser into the oxide layer on top of the wafer it was suggested we use gold nanoparticles. I was tasked with modelling...

I tried: Initial energy= ##E_{C1} + E_{C2}= 1/2C(4V_0) +1/2 (3C)(9V_0)= 31CV_0^2/2## this energy will be completely converted to magnetic energy in the inductor when the current through it is maximum. Final energy= ##1/2 Li_{max}^2## Equating the two and solving, I get ##i_{max}= \sqrt{31C/L...

I am very confused, all i have thought about right now is that, in that isolated branch connecting A, B and C, the net charge would be conserved. Not sure how to proceed. I feel that, if there is a charge ## -Q ##at A, and a charge ##-Q_1 ## at B, then the charge at C MUST be ## Q+Q_1 ## maybe...

So, I was just doing some practice on Gauss's law, and most of the questions, when I needed to take the surface integral of something, it would be something simple, like a sphere, cylinder or at worst a torus. Though it's impractical (and probably useless) - it got me wondering, what would...

Suppose there are two reference frames. One is rotating with respect to another with rotational velocity ##\omega##. Now if in one of the reference frames the vector potential is $$(1, 0, 0, 0)$$ then in the other reference frame it will be $$(\sqrt{1-(\omega r)^2}, 0, \omega r, 0)$$. Now in...

I have a Hamiltonian $$ H = \frac{1}{2} g^{\alpha \beta}\left(p_\alpha- A_\alpha\right)\left(p_\beta- A_\beta\right) $$ I want to calculate the equation of motion. How can I calculate the equation of motions $$ \frac{dx^\mu}{d\tau} = g^{\mu\nu}(p_\nu - A_\nu) $$ This one is straight...

It is well understood that an infinite monochromatic, circularly-polarized electromagnetic plane wave has no angular momentum density. However, a finite monochromatic, circularly-polarized electromagnetic plane wave packet does have an angular momentum density, arising from effects at the border...

In an infinite plane wave propagating in the ##z## direction, the momentum density is ##\mathbf{p}=(4π)^{-1}(\mathbf{E} × \mathbf{B})## which points in the ##z## direction; therefore, the angular momentum density about the ##z##-axis ##\mathbf{L} = \mathbf{r} × \mathbf{p}## has no...

I believe that if a put current through a coil of wire and if I have unlimited power to force through that current and if the coil can accept unlimited power without being degraded, I could produce a magnetic field in a vacuum of unlimited strength-is that correct? But supposedly if I applied...

David J. Griffiths Introduction to Electrodynamics page 460: Lorentz force equation invariance leads to different Lorentz force values in different inertial frames. Is this a problem for conservation of momentum? More specifically conservation of angular momentum?

Using Faraday's law we have $$\mathcal{E}=\oint\vec{E}\cdot d\vec{l}=\frac{Q}{C}+IR=-L\dot{I}\tag{1}$$ where ##I=\dot{Q}##. After rearranging the expression we get $$\ddot{Q}+\frac{R}{L}\dot{Q}+\frac{1}{LC}Q=0\tag{2}$$ $$\ddot{Q}+\gamma\dot{Q}+\omega_0^2Q=0\tag{3}$$ If the system is...

I'm following this tutorial I noticed that he provided the boundary values in FEMM but he didn't provide the Laplace equation ##\dfrac{\partial^2 V}{\partial x^2} + \dfrac{\partial^2 V}{\partial y^2} = 0## for the field but it is still corrected simulated? or is it not necessary to provide it...

I found Physics Forums via Google search. I'm a Tanzanian citizen pursuing a bachelor's degree in Physics (minor in Economics) at The Open University of Tanzania. I'm a first year undergrad. I'm glad to be a part of a huge community of like-minded people. I'm especially passionate about...

I know what ##\Phi## and B are, I think they are the magnetic flux and its density. I think ##\mu## is the permeability. But I dont know what ##R_c## and MMF are and how are these formulas deduced.

TL;DR Summary: Ping-pong ball hanging static from infinite plane of charge and a string Really struggling with this question. I'm not sure if I have set up the free body diagram correctly and don't know how to set up the x and y components

A week ago, I started studying electromagnetism. I was introduced to a few new concepts and one of them was H. Now, in my book, they defined H as just magnetic field strength and B as magnetic induction. The thing is, I don't understand what those terms really are (in a physical way), let alone...

For the past few months, I've been on a look out for the best physics community on the Internet and I've just come across this one. My primary goal is to gain as much knowledge as possible in the area of classical mechanics and electromagnetism in a year. I'm fairly new to magnetism, but I can't...

Here is a chapter from MIT OCW's 8.02 Electromagnetism course. At the end of page 14 is section 13.6 "Poynting Vector". The calculations I am interested in are on page 15. There is a passage that seems to have a typo in it. Let me try to show why despite recognizing a typo I am unsure of what...

Apparently, the direction of wave propagation is the direction of ##\vec{E}\times\vec{B}##. From what I have seen so far, given Maxwell's equations, the set of solutions giving plane waves has the characteristics that 1) electric field has only a component in the ##y## direction 2) magnetic...

My initial thought was to model the wave as $$y(x,t)=Ae^{-B(x-t)^2}$$ This question is part of an automated grading system and the above entry is considered incorrect. I think I need to incorporate the information that the speed of the wave is ##v## somehow.

Hello everyone. I am new to this website but not new to physics. I took physics in high school and college, but I did forget a lot of what I learned. I graduated from college with a degree in Electronics Engineering. I graduated in 1997. The areas of physics that I am the most interested in is...

I can find the magnetic induction vector of the first conductor at a given point using the formula (its 6,667*10^-7 Tl) but I don’t understand what needs to be done with the second conductor. I have come across similar problems in which, however, the distance from the second conductor to the...

I have been taught topics in high school circling around Newtonian mechanics and some basics of work and energy, waves, geometric optics, current and circuits and some poor electrostatics and unclear concepts of modern physics. I realize that I have significant weak areas in Physics and I aim...

I’ve been trying to get the proper understanding of electric field. Fine I get the definition: any charge changes space around itself and thus generates electric field that acts with force on any object that’s relatively close to the charge. But first from the first, how can the FIELD act with...

I'm an ordinary college student who likes physics, engineering mathematics, and electromagnetism. I'm not sure because it's my first time participating in an overseas forum, not a domestic one, but I look forward to your kind cooperation.

In this situation I would have two solenoids facing each other, such that both ends are north for example, and when activated they are actively experiencing repulsion, I know that the magnetic field of both would decrease in strength, but would there be any affect on the electrical input of each...

In my electrodynamcis assignment I'm being asked to derive the wavelength of the normally polarised wave transmitted through a glass/air interface as a function of ##n_1## (the refractive index of the first medium) using the concept of phase continuity and the fact that maxima should be equal at...

My question is about item (b). For item (a) we have uniform circular motion in the regions with uniform magnetic field. $$\vec{F}_{B_1}=qv\hat{\theta}_1\times B_1(-\hat{k})=-qv_1B_1\hat{r}_1=-mR_1\theta'^2\hat{r}_1\tag{1}$$ $$B_1=\frac{mv_1}{R_1q}\tag{2}$$ A similar calculation for the...

Between ##t_1## and ##t_2## the magnetic flux is positive and increasing. Thus, we have a negative emf and from the point of view of the little stick figure above, the induced current is clockwise. It is not clear to me where the repulsive force on the approaching magnet comes from. The...

In "The Strange Story of the Quantum", Banesh Hoffmann writes: What was that contradiction?

When extending general relativity to include electromagnetism, several authors (e.g. Novello, Sabbata ecc.) assume that the traceless part of the torsion tensor vanishes or is deliberately set to zero. Then, either the trace or axial part of the torsion is used in association with the...

I originally thought that this problem was simple, and it still seems like it is, but there are conflicting solutions and I don't know which is correct. So I first solved for R1 and R2 using V=kQ/r where R1 is 0.514 and R2 is 0.54. My original thought was volume is conserved so V1 + V2 = V3 and...

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For the multipole expansion of the electric potential, we expand ## \frac 1 {|\vec r-\vec r'|}## in the following way: $$\frac 1 {|\vec r-\vec r'|} = \frac 1{\sqrt{(\vec r-\vec r')^2}} =\frac 1 {[ \vec r^2 +\vec r'^2 -2\vec r\cdot \vec r']^{-\frac 12}}=\frac 1{[\vec r^2 + \vec r'^2 - 2|\vec...

in this text: my question is in highlighted line: "The two rods have the same length (in S) and contain the same number of charges." why? Considering that the negative rod has movement, it should have a shorter length than the positive rod according to a relativity!

In my lectures, we have derived the dispersion relation $$ |\vec k|^2 = \frac {n^2 \omega^2}{c^2}$$ by substituting in a plane wave solution for the electromagnetic wave, into the wave equation derived from the Maxwell equations $$\Delta\vec E= \mu_0\epsilon_0 \frac {\partial^2 \vec...

I think I managed to solve the entire problem, as I show below. My main doubt is about item (e), the incremental circuit. Part (a) Using the node method and KCL we reach $$\frac{v_I-v_A}{2}=10(1-e^{-v_A/5})\tag{1}$$ Part (b) We can simplify (1) to $$v_A=5\ln{\left ( \frac{20}{v_A+20-v_I}...

Part (a) The circuit in figure 1b is linear. It is a simple voltage divider circuit. The relationship between a voltage source ##V_I## and output voltage ##V_O## is $$V_O=\frac{R_LR_{IN}}{R_L+R_{IN}}V_I$$ This relationship is true individually and independently for the DC voltage source and...

Here is the circuit. Note that no current flows between the left and right sides of the circuit: their only relationship happens through the MOSFET that is parallel to B. There are eight cases to consider: all the combinations of ON/OFF for the three MOSFETs. Here is a summary of the eight...

The first thing I thought about was the relationship ##\vec{J}=\frac{\vec{E}}{\rho_r}## which is a statement of Ohm's law. That is, current density is proportional to electric field and the constant of proportionality is the reciprocal of resistivity ##\rho_r##, which is the same as...

We have motivated the derivation of the vector potential in the following way: However, I cannot understand where the ##-## sign in the second equality came from. I thought that it was because the gradient was with respect to the ##y##-variable, and then using the product rule one could...

The work done by the electric field when we bring a charge ##dq## from an infinite distance to the surface of a shell with radius ##r## is $$dW=\int_{\infty}^r \frac{Qdq}{4\pi\epsilon_0 r^2}dr=-\frac{Qdq}{4\pi\epsilon_0r}\tag{1}$$ The work done by the electric field to charge a spherical shell...

Let me first think about a simpler case. Suppose we have a capacitor. That is, the two plates have charges of equal magnitude and opposite signs. Consider the purple rectangle which represents a Gaussian pillbox. The electric field due to one of the plates individually has field lines...

I drew the magnetic field lines. The setup was like this: The needle below AB was in the same plane so above AB we get the magnetic field pointing inwards then looping all over Ab from behind the emanating from below AB i.e. pointing outwards. The needle is kept at that point from which the...

I was just thinking that if we keep the wire in, suppose, XZ plane and the magnetized needle also in XZ plane. Then in which direction will the needle point? we're going to have either +j cap or -j cap direction by drawing out the tangent at the point where the needle is kept. But a needle could...

As shown in the diagram, a copper conductor is placed over two stretched copper wires whose ends are connected to a D.C. supply. What should be the magnetic poles at points A and B lying on either side of the conductor to experience the force in the upward direction?-------------------- My...

We have the following constitutive relations: $$ \vec D= \epsilon_0 \vec E +\vec P$$ $$\vec B=\mu_0\vec H + \vec M$$ And Maxwell's equations are: $$\nabla\cdot\vec D = \rho$$ $$\nabla\cdot \vec B=0$$ $$\nabla\times\vec E=-\frac{\partial\vec B}{\partial t}$$ $$\nabla\times\vec H=\vec j...