Field Definition and 1000 Threads

This problem honestly got me in big confusion. I managed to find the angle ##\theta## at which the rod rests by equalling the components of weight and Lorentz's force... but from this point on I really don't know how to manage the harmonic oscillation part.

With free part L=-½(∂Φ)^2 -½m^2 Φ^2 and interaction term L=½gΦ^2Any help would be appreciated, thank you.

here is the situation Hi guys, I should illustrate the motion of an electron in both cases, but I cannot really understand how will the field be like in the gap between the two(filled) hemispheres(conductor and non). Another thing is: for the conductive hemispheres, does it make any sense to...

Okay, so, the magnetic field lying(parallel) to the plane of the coil is confusing me quite a bit. Usually, in this kind of problem, we have a magnetic field directed perpendicularly to the plane. Considering this orientation of the field, wouldn't the torque on this sort of "elementary brush...

Hello PF, I am about to defend my PhD in some area of Physics/Materials Science. I am also currently working at a company, but I want to resign after I defend my PhD thesis. I am offered a postdoc position and a salary raise if I stay in my current company but I feel I would mostly apply some...

The Poynting vector $$\vec S=\frac{1}{\mu_0} \vec E \times \vec B$$ gives the power per unit area. If I need this in terms of electric field only,I should be able to write B=E/c (for EM wave) Assuming they're perpendicular, ##S =\frac{1}{\mu_0 c}E^2##. Now, ##c=\frac{1}{\sqrt{\mu_0 \epsilon_0}}...

I'm following the lecture notes by https://www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf. On page 169, section 6.2 he is briefly touching on the non-abelian gauge symmetry in the SM. The fundamental representation makes sense to me. For example, for ##SU(3)##, we define the...

$$B = \frac {\mu_0 I}{2 \pi r} $$ By Right-hand Grip Rule, the direction of the magnetic field by wire in y-axis is into the paper (z) while the direction of the magnetic field by wire in X-axis is upwards (+i) The answer state the Magnetic field is in the (i - y) direction though. Next...

All I'm reallly confused on this problem is what the expression for the emitted field is. As long as I've got that, I'm good to go, but I just don't know what to use. I've tried looking for an expression for the emitted field but I've had no luck. Would appreciate any ideas or someone telling me...

From my understanding, quantum fluctuations create particle pairs that are usually annihilated. Is it possible to use some kind of force (eg: electromagnetism) to direct and separate antiparticles from normal particles? I believe experiments have proven that it is possible to store positrons...

Could somebody check my solution?

hi guys this seems like a simple problem but i am stuck reaching the final form as requested , the question is given the magnetic vector potential $$\vec{A} = \frac{\hat{\rho}}{\rho}\beta e^{[-kz+\frac{i\omega}{c}(nz-ct)]}$$ prove that $$B = (n/c + ik/\omega)(\hat{z}×\vec{E})$$ simple enough i...

From one point of view the charged particle is accelerating and should emit electromagnetic waves. But from the equivalence principle, I think, it should not. Does anybody know the answer?

I am trying to derive that $$\nabla \times B=\mu_0 J$$ First the derivation starts with the electric field $$dS=rsin\varphi d\theta r d\varphi $$ $$ \iint\limits_S E \cdot dS = \frac{q}{4 \pi \varepsilon_0} \iint\limits_S \frac{r}{|r|^3} \cdot dS $$...

I couldn't prove the first one but i tried to find the period F = -dU / dx = - d( U0tan^2( x / a ) ) / dx = - U0 ( ( 2 sec^2( x / a ) tan( x / a ) / a ) with F=d^2x/dt^2, tan(x/a)=x/a we have d^2x/dt^2 + U0 ( ( 2 sec^2( x / a ) ( x / a^2 ) =0 from there i don't know how to handle the...

I am trying to design an electromagnet which consists of a copper PVC sheathed wire wound around a cylindrical plastic spool of Circumference (C) = pi x diameter. The spool has a hollow body of diameter D1. This wire has maximum length (L), cross sectional area A, resistivity P. The spool once...

The Lorentz's force acting on a charged particle perpendicularly "hitting" a magnetic field will be directed upwards, and generally directed towards the center of the circumference traveled by this particle, and so will cause a centripetal acceleration to keep it in a circular motion. By...

I know the answer is ##ka^3/2##. I got ##ka^2## and I don't know how to get the right answer. I saw an explanation using integrals, but my class is algebra-based. My attempt: ##Flux=ABcos\theta##. I figure ##cos\theta## is 1 becuase the angle between the magnetic field and the normal to the...

It seems a gravitational field does not alter the electromagnetic field strength. Is this correct? My reasoning: With no gravity, field strength is: F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu Introduce gravity: \partial_\mu A_\nu \rightarrow \nabla_\mu A_\nu = \partial_\mu A_\nu +...

Hello there, I've worked through this problem and I would just like to check whether I've understood it correctly. I found ##\vec H##, ##\vec B## and ##\vec M## using Ampere's Law and the above relations as I would for any thin current carrying wire and these were my answers: $$\vec H = \frac I...

If ##\tau= 0.0727, N=60, i=1.3, B=1.0,## and ##\theta=15##, I tried the following calculation: ##\tau=NIABsin\theta## ##\tau=NIs^2Bsin\theta## ##s^2=\frac {\tau} {NIBsin\theta}=\frac {.0727} {60*1.3*1*sin(15)}=0.0632 m=6.32 cm## The answer is probably right in front of me, but I don't know what...

In the picture below, the direction of the magnetic field lines can be determined by using the right-hand rule with the thumb pointing in the direction of the current. If we use the right hand rule in the picture below, thinking of the yellow arrow as the current, we would not get the correct...

Let us suppose we have a scalar field ##\phi##. The Klein-Gordon equations for the field can be written as \begin{equation} \ddot{\phi} + 3H \dot{\phi} + \frac{dV(\phi)}{d\phi} = 0 \end{equation} The other two are the Friedmann equations written in terms of the ##\phi## \begin{equation} H^2 =...

Summary:: I am trying to derive that the divergence of a magnetic field is 0. One of the moves is to take the curl out of an integral. Can someone prove that this is addressable Biot Savart's law is $$B(r)=\frac{\mu _0}{4\pi} \int \frac{I(r') \times (r-r')}{|r-r|^3}dl'=\frac{\mu _0}{4\pi}...

We have two different accepted formulas for the far field and near field respectively. I want a numerical program that works for both, furthermore I want to use it to calculate power through the aperture after confirming it in the far field vs near field. I start off by treating the far field...

Attempt at solution: a) Since I need help with b) this section can be skipped. Results : ##ρ_{psa} = -Pa ## ##ρ_{psb} = Pb ## ##ρ_{p} = \frac {-1}{R^2} \frac {∂(R^2PR)}{∂R} = -3P ## b) This is where I am unsure (first time using gauss law for P) so I need some confirmation here: ## \int...

Hello All, Does anyone here have degrees that aren't related to their careers? I was thinking of maybe taking some automotive courses at a community college towards an associates. This is merely for my own interests, and to allow me to work on my own car, knowing that I did the job correctly...

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Assume that a certain charge distribution ##\rho## generates an electrical field ##E_{ext}## in the surrounding space. We also note the corresponding generated potential ##V_{ext}##. Assume furthermore that a conductor A, with a definite shape and volume, is placed in field ##E_{ext}##, and is...

I am analyzing the rotor magnetic field, i feel i understand the basic concept but have few clarifications. At pt1, the net mmf due to currents ##i_a = i_{max}; i_b = -\frac{i_{max}} 2 ; i_c = -\frac{i_{max}} 2## is ##\frac {3F_{max}} 2## Similarly i can do for Pt2. But my confusion is the...

I have the problem with my solution. I don't know it is correct. Could somebody check it?

In part c, plotting the vector field shows the vector field is symmetric in x and y in the sets {x=y}. in {x=y}, the variables can be interchanged and the solution becomes x = x°e^t y = y°e^tHowever, these solutions do not work for anywhere except {x=y} and don't satisfy dx/dt = y and dy/dt =...

My answer will be no for both (a) and (b) because there is no change in magnetic flux experienced by the circular coil. Am I correct? Thanks

figure 1: → I don't understand how to approach this problem. Basically it asks for the distance r.I think I should use Gauss's law, but I've been thinking about the shape of the gaussian surface and I'm not sure about how it should look or where I should place it. Any help would be useful...

We usually think about atomic orbital as wave(function), but it was created from e.g. electron and proton approaching ~10^-10m (or much more for Rydberg atoms), and electron has associated electric field. This wavefunction also describes probability distribution for finding electron (confirmed...

My attempt at a solution is shown in attached file "work for #10.png". I used Desmos Scientific online calculator to obtain my final answer.

Hello, I am looking for some information on how 2 different types of magnetic fields interfere with each other. And i don't mean, 2 magnets, but let me be specifically: Lets say that you have a very strong static magnetic field, from a huge magnet. (for instance, the strength of the magnet of...

Does any researcher/scholar/professor here ever feel stuck with the field they have chosen to pursue? Do you ever feel it's too late to switch or regret not choosing something else while studying?

What is an interpretation of wave of field(wave that its medium is field) in QFT?Is it correct that the trajectory that wave propagates is the "classical trajectory" of particle created by the field?

I understand how the weaker and stronger field occurs but I don't understand why the force on the wire is directed from stronger to weaker field. I mean why not from weaker to stronger? I also want to ask about Newton's 3rd law in this case. Newton's 3rd law states that for every action there...

This is not a homework question but something that bugs me a bit. My professor has stated that the electric field inside a conductor is 0. This I understand. However, he has also said that even if the conductor has some hole in it, the electric field inside this hole is also 0 Now, two...

p=Bqr and del p = p del theta

It is a wonderful book for learning QFT. Interesting problems with detailed solutions. I have tried the problems from chapter 1 to chapter 7. In most chapters, I could at least solve some part of the problems. But I got stuck in chapter 4, the Dirac equation. I could not solve any of the...

I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?

I tried approaching this by finding the tangential and normal electric fields. Is this the correct approach? I've attached a drawing of the surface provided. ##\oint_S E \cdot dl=0## ##E_{tan1}\Delta x-E_{tan2}\Delta x=0## We know that ##E_{tan1}=E_{tan2} Next, we can find the normal...

The current direction is as follows I think so much and do the right hand rule i get 0 at the center, but not sure why the answer is non zero. I have shown the directions of the magnetic fields, i have not shown the magnitudes of equal length but they all are equal. Why the answer is non zero...

Untill now i have only been able to derive the equations of motion for this lagrangian when the field $$\phi$$ in the Euler-Lagrange equation is the covariant field $$A_{\nu}$$, which came out to be : $$-M^2A^{\nu} = \partial^{\mu}\partial_{\mu}A^{\nu}$$ I have seen examples based on the...

For the first part, since $$ E(r) \propto \frac{1}{r} \hat{r}$$ by the principle of superposition the maximal electric field should be halfway in between the two wires. Then I'm not sure how to go about the second part of the question. I understand that the total potential due to the two wires...

x and y are different than 0 As you can check, rot (del x F) is equal zero. Immediately someone could imagine this is a conservative field. But it is not, it is not path independent in certain occasions. I just know one way, involving polygonal, but there is not another way to check if F is...

It is not a direct home work problem, i was thinking if a sine wave current passes through the straight current carrying conductor, what will be the magnetic field. For the DC current I know the formula as below. ##B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}## Let the current be ##I =...