Field Definition and 1000 Threads

In a general coordinate system ##\{x^1,..., x^n\}##, the Covariant Gradient of a scalar field ##f:\mathbb{R}^n \rightarrow \mathbb{R}## is given by (using Einstein's notation) ## \nabla f=\frac{\partial f}{\partial x^{i}} g^{i j} \mathbf{e}_{j} ## I'm trying to prove that this covariant...

Hi. A electromagnetic wave consists of an electric and a magnetic component. I believe that the electric field strength is measured in volts per meter. The magnetic field I think is measured in Tesla. Let's imagine that I measure the electic field strength of two different radio stations and...

I've just started Quantum mechanics by McIntyre and have understood the following about operators which the author wrote till chapter 2: Each observable has an operator Operators act on kets to produce another kets. Only eigenvalues of an operator are possible values of a measurement. Now...

Consider an uncharged particle with spin one-half moving with speed ##v## in a region with magnetic field ##\textbf{B}=B\textbf{e}_z##. In a certain length ##L## of the particle's path, there is an additional, weak magnetic field ##\textbf{B}_\perp=B_\perp \textbf{e}_x##. Assuming the electron...

According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing?? see figure below The answer should be Ex = 2*k*lambda / r...

From the second equation I get that, ##\vec D =\frac{q}{4\pi \vec r^2}\hat r## From first equation I get that ##\vec E = \frac{q}{4\pi \vec r^2 \epsilon}=\frac{q}{4\pi \vec r^2 K \epsilon_0}## But I saw that the answer is ##\vec E=\frac{\vec E_0}{K}## While writing the comment my mind said...

The dielectric strength of air (ie the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becoming electrically conductive) is 3 000 kV ( https://en.wikipedia.org/wiki/Dielectric_strength#Break_down_field_strength ). In...

Say we are working in a 2D plane, with a camera and a ball flying past as shown. Camera at bottom, ball flying from left to right Given that I have the X/Y coordinates of the camera, as well as the coordinates of the ball at any given time during the 'flight', how am I supposed to calculate the...

When I try following numbers from internet then I don't get an expected answer. ## \mu_0 = 1.25663706 × 10-6 m kg s^{-2} A^{-2}## ##q =1.60217662 × 10^{-19} coulombs ## ##r=2.82x10^{-15} m## Velocity of that electron is given in question ##\vec v= 2 \times 10^6 \\ \mathrm{ms^{-1}}##Since...

Say there is a gas made up of two gas molecules: Molecule A and Molecule B. Molecule A has a mass: ma and mole fraction: na. Molecule B has a mass: mb and mole fraction: nb. The gas is at thermal equilibrium and has a constant temperature throughout itself (T) everywhere. It is placed in a...

As far as I can tell, the shape looks like a cuboid with 8 arms pointing in all directions.

If I want to carry 10 A through an 8 AWG wire, I understand that there will be a specific magnetic field around the wire which will decrease as I move outward from the wire radially. Let's consider the center of that wire as coordinates (x,y)=(0,0). An object located at (0,10) would see a...

So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. I have been told to calculate the potential difference ##VC - VA##. According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. But I say it's ##-20 V## as...

I was just wondering how much work is being done in the field of quantum gravity nowdays. Is there still a huge volume of research published on the topic? Are we closer to a "solution" nowdays than we were a few years ago? And also, what exactly would constitute a solution to such problem?

Please be kind to help

Hi all, I am trying to work through the Unruh Effect for the (1+1)-dimensional massive scalar field case and came across the paper I attached. However, I am trying to derive equation 5.68, but am greatly struggling with the prefactor on the left hand side. When comparing the left hand side to...

Hey guys, I just wanted to know if you think that a membrane field theory could ellucidate the non-perturbative framework of M-theory? Let me specify and explain what I mean by that: String field theory was intoduced to study the non-perturbative regime of string theory and some achievements in...

Hi everyone, It is about the quantization of the electromagnetic field. The expression of field E and B are defined with: -the annihilation a- and creation a+ operators, and the frequency ω. So my question is: how does these fields must be expressed if they where "static"? I mean, how the...

Having exceeded the limits of Excel to track the names, rank, attributes, etc. of a list of ship's crew, I have tried to use Access. First up... I'm not a database expert. So, I'm muddling along with help from YouTube, but either I can't frame a correct search for this problem or it's not...

It is given that a theory is invariant under the length scaling:\begin{align*} x &\rightarrow \lambda x \\ \phi(x) &\rightarrow \lambda^{-D} \phi(\lambda^{-1} x) \end{align*}for some ##D## to be determined. The action of a real scalar field is here:\begin{align*} S = \int d^4 x...

Hi all, I am currently trying to prove formula 21 from the attached paper. My work is as follows: If anyone can point out where I went wrong I would greatly appreciate it! Thanks.

Hi, I was reading this insight schwarzschild-geometry-part-1 about the transformation employed to rescale the Schwarzschild coordinate time ##t## to reflect the proper time ##T## of radially infalling objects (Gullstrand-Painleve coordinate time ##T##). As far as I understand it, the vector...

Proof of 84i): We assume that ##E/F## is a field extension. For each ##i##, ##F(\alpha_i)## is the smallest subfield of ##E## containing ##F## and ##\alpha_i##. Let ##F'## be a subfield of ##E## containing ##F## and ##\alpha_1, \dots, \alpha_n##. Then ##F'## containing ##F(\alpha_i)## for all...

Hello all, I have a question on a pivotal concept of GR that I've never managed to fully grasp. In what coordinate system is the Einstein's Field Equation set up and solved? I've always assumed it's an Euclidean 4D space, whose metric is irrelevant because we are dealing with scalar...

Electric Flux = E*A = 5*6(0.05)^2. when i look up at other sources they use Electric flux = q/ (8.854*10^-12 [this is e]) equation but I am confused on why the E*A equation don't work. The answer is 0.02Nm^2/C

Hello for everyone. I have a question according the field distribution in the semiconductor while the field effect. According to logic, the field is scrreened due to the field of the polarized carriers like electrons and holes. I know about the Debiye length. And that the field on the infinity...

As shown in figure below, the electric field E will be normal to the cylinder's cross sectional A even for distant points since the charge is distributed evenly all over the charged surface and also the surface is very large resulting in a symmetry. So the derived formula should also apply to...

As $$\hat{P_i} = \int d^3x T^0_i,$$ and $$T_i^0=\frac{\partial\mathcal{L}}{\partial(\partial_0 \phi)}\partial_i\phi-\delta_i^0\mathcal{L}=\frac{\partial\mathcal{L}}{\partial(\partial_0 \phi)}\partial_i\phi=\pi\partial_i\phi.$$ Therefore, $$\hat{P_i} = \int d^3x \pi\partial_i\phi.$$ However...

Hello everybody! I have a question concerning the Fourier transformation: So far I have experimentially measured the magnetic field of a quadrupole but as the hall effect sensor had a fixed orientation I did two series, one for the x, one for y component of the magnetic field, I have 50 values...

Proof: We will first show ##\gcd(p(x), p'(x)) = 1##. Define ##d(x) = \gcd(p(x), p'(x))##. Then we can find ##q(x) \in F[x]## such that ##p(x) = d(x)q(x)##. But ##p(x)## is irreducible which means ##d(x)## is constant or ##q(x)## is constant. If ##q(x)## is constant, then ##\deg d(x) = \deg...

From Wikipedia: Which should be conceptually similar of what happen in the non-relativistic limit of the Dirac equations when you see that the solutions decouple. Do you have any reference that I can look up where the derivation for the KG field is performed? Thanks in advance!

Hello all, what would happen to a perfectly conducting cylinder immersed in a rotating magnetic field, with the rotation axis parallel to that of the cylinder? I guess the cylinder would start to rotate with the field? Right? Thank you

These are the vector fields. I really have no idea how to see if there is a curl or not. I have been looking at the rotation of the vector fields. The fields d and e seem to have some rotation or circular paths, but I read online that curl is not about the rotation of the vector field itself...

Question: My attempt: Could someone please confirm my answer?

Hi, I would like to ask for a clarification about the difference between a differential k-form and a generic (0,k) tensor field. Take for instance a (non simple) differential 2-form defined on a 2D differential manifold with coordinates ##\{x^{\mu}\}##. It can be assigned as linear combination...

It is given that the charge density of a particle of charge ##q_0##, world line ##z^{\mu}(\tau)## (and 4-velocity ##u^{\mu}##) in a spin-##s## force field is a ##s##-tensor\begin{align*} T^{\mu \nu \dots \rho}(x^{\sigma}) = q_0 \int u^{\mu} u^{\nu} \dots u^{\rho} \delta^4[x^{\sigma} -...

The attached probem tricked me because the answer is apparently D and not A. Presumably because the magnetic field is weaker with 2 bar magnets joined N/S compared to a single bar magnet. So this seems to be a gap in my knowledge as to the resulting strengths of magnets joined together. Are...

Hi, I'm a current senior in college, and am applying to grad. schools for fall 2022. I'm interested in high energy theory, and I have had some research experience in ads/cft correspondence, kaluza-klein theory, computational particle physics. However, I'm not certain as to which particular topic...

Question: Relevant Equations: My attempt: Could someone please confirm my solution?

What am I missing? I also don't get the title of the section: "Charge distributions with enough symmetry for Gauss's Law". I thought Gauss's Law was valid for any closed surface enclosing a charge. I don't understand what "enough symmetry" means in the title above. I get that with symmetry...

Using Gauss's Law By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane. We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox". The charge enclosed is...

[Moderator's Note: Thread spin off due to topic and level change.] For a spherically symmetric solution, if SET components were written in terms a single one of 4 coordinates, in a way plausible for a radial coordinate, the I believe solving the EFE would require spherical symmetry of the...

Hey, I was trying to figure out this problem. I got (a) using B = mu * NI/L but I'm not sure how to start the part about the magnetic field in the gap after the solenoid is ripped in half with 1 cm gap. Thanks for the help!

We can analysis a static EM field into Fourier serie. Then we can consider a static EM field as a superposition of many running EM wave. So why we could not consider static EM field as a superposition of many photons(maybe virtue photons)?

Hi all, (I also posted this in the high energy theory section since my impression is there is a deep interplay between modern condensed matter theory and high energy theory). Some background: I'm interested in the interplay between condensed matter and high energy theory. I'm a bit more than...

Hi all, my work is shown on the attached image. The boxed equation is what I get to but I do not understand how to go from there to what the book has. I am guessing that the problem arises when trying to solve the cross product. I understand that I will need to find the value of the sine of the...

I am interested in particular in the second integral, in the ##\hat{r}## direction. Here is my depiction of the problem: As far as I can tell, due to the symmetry of the problem, this integral should be zero. $$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$ I don't believe I need to...

The strategy will be to figure out what ##dq##, ##\hat{r}_{dq,p}##, and ##r_{dq,p}## are, plug them into the expression for ##d\vec{E}_{p_r}##, then integrate over ##d\vec{E}_{p_r}## to obtain ##\vec{E}_{p_r}##, the electric field at ##P## due to the arc on the right. Then I will repeat the...