Field Definition and 1000 Threads

All physical laws have to be Lorentz invariant according to a lecture I just watched. Why is general covariance (which is more general than Lorentz invariance) not a requirement for all laws of physics? Are there any quantum gravity theories that take the approach of adding general covariance to...

Hello, I was glazing through what I would consider an advanced physics textbook and I saw this image. It is a schematic picture of an alpha-particle in a field of an atom. Now, can someone get me started on what (and why and how) is going on in it? Especially with the fraction with pi.

A classic example in textbooks is calculating the magnetic field inside a solenoid of length ##l## with ##N## turns and making the assumption that the magnetic field inside the solenoid is pretty uniform and outside it is 0. Using Ampere's law ## \oint_C \vec B \cdot d \vec l = \mu_0 I_{through}...

The beam of protons are directed towards the axis of the cylinder, perpendicular to the direction of the field. While traveling through the cross-section of the cylinder, the proton beam experiences a magnetic force, which tends to move the beam in a circular orbit of the radius given by: r =...

So for the Gaussian theorem we know that $$ \frac{Q}{e} = \vec E \cdot \vec S $$ Q's value is known so we don't need to express it as $$Q=(4/3)\pi*(R_2 ^3-R_1 ^3)*d$$ where d is the density of the charge in the volume. I've expressed the surface $$S=4\pi*x^2$$ where x is the distance of a point...

Let point charge q be at y=r. Let there be an infinite conducting plane along the x-axis and z-axis that is neutrally charged. In this case, the method of mirror charges can be used. The plane is replaced by a point charge -q at y=-r. The electric field for y > 0 is the same in both cases...

We relating to an electromagnetic radiation as waves. and in waves there is maximum point and minimum point but when there is permanent electromagnetic level there is no disorder or weave . so is it possible to measure it in blank space relative to other places

Hi, I have been studying Quantum Field Theory this semester! It seems that Shwartz and Peskin are the most popular choices when it comes to studying QFT. But apparently my professor have another "old" preference. He strongly suggested that we learn QFT from Zuber's book. I have looked at the...

I first found the Lorentz force on the ball as a whole$$\vec{F}_m = \iiint_V \rho(\omega \times \vec{r} + \vec{V})\times \vec{B} dV = \rho \vec{\omega} \times \left( \iint_V \vec{r} dV \right) \times \vec{B} + \rho \iiint_V \vec{V} \times \vec{B} dV = Q\vec{V} \times \vec{B}$$due to the...

So the magnetic field induced at the center of a current-carrying loop is given by: B = μ0 i /2r where r is the radius of the loop In the case of a semi-circular loop, this becomes B = μ0 i /4r In the question, i = 2A, r1 = 1m and r2 = 2m So, field induced at the center of first semicircular...

I have an older 12 volt battery-charging 1979 Sencenbaugh wind generator that I am testing. It has an 3 phase alternator with a field winding that must be excited, as opposed to the newer "permanent magnet" alternators. The manual says that 60 watts maximum should go to the field winding...

How did you find PF?: Surfing web Can someone advise on this? In most diagrams showing how mass effects the gravitation field (earth for instance), bending fabric of space, it is demonstrated on one plane. Why is it shown this way and is there any other way of illustrating this?

[Ref. 'Core Concepts in Special and General Relativity' by Luscombe] Let ##M,M'## be manifolds and ##\psi:M\to M'## a diffeomorphism. Even if ##\psi## weren't a diffeomorphism, and instead just a smooth map, the coordinates of the pushback of ##\mathbf{t}\in T_p(M)##, would be related to the...

-------------------------------------------------------------------------------------------------------------------------------------------------- This was a problem introduced during my classical electrodynamics course. I am not 100% sure, but I think I've solved up to problems (a) and (b) as...

Suppose you are analyzing this image. The question to answer is: Explain why the alpha particle's path has a larger radius than either of the beta particle paths. Justify your answer using either momentum or charge-to-mass ratio. When you are answering this, suppose you know that , in...

Similar to what is shown here, except the south side would be the weak side of the array. A link to purchase one of these or at least the magnetic field arrangement would be very helpful. Thanks in advance.

My solution is making an analogy of the ##\text{Relevant equations}## as shown above, starting from the equation ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##. We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times...

I'm reading about the Stern–Gerlach experiment and the only part that confuses me is how a magnetic field would deflect particles with magnetic dipoles instead of just rotating them. In this case the magnetic field is non-uniform, but it still seems intuitively strange to me since magnetic...

I'm a bit confused about the condition given in the description of the symmetry transformation of the filed. Usually, given any symmetry transformation ##x^\mu \mapsto \bar{x}^\mu##, we require $$\bar\phi (\bar x) = \phi(x),$$ i.e. we want the transformed field at the transformed coordinates to...

Suppose we have a Hamiltonian containing a term of the form where ∂=d/dr and A(r) is a real function. I would like to study this with harmonic oscillator ladder operators. The naïve approach is to use where I have set ħ=1 so that This term is Hermitian because r and p both are.*...

Say I've got a magnet flying through empty space in a homogenous magnetic field. The magnet precesses and flies in a straight path. Now make that magnetic field inhomogenous. The magnet precesses and flies in a curved path. What I can't figure out is why the path is curved. It is because...

I've been studying Tong's beautiful chapter (pages 106-109; See also Peskin and Schroeder pages 52-58), together with his great lectures at Perimeter Institute, on how to quantize the following Dirac Lagrangian in the wrong way $$\mathscr{L}=\bar{\psi}(x)(i\not{\!\partial}-m)\psi(x) \tag{5.1}$$...

I am new to this forum, and this is my first post. Please bear with me if my query has any inaccuracies. In the attached figure, a coil is wrapped around the central arm of a flat H-shaped thin metallic plate (such as iron). DC current flows through the coil and magnetizes the arm. At the...

Wikipedia defines the derivative of a scalar field, at a point, as the cotangent vector of the field at that point. In particular; The gradient is closely related to the derivative, but it is not itself a derivative: the value of the gradient at a point is a tangent vector – a vector at each...

Suppose that we have an insulating cylinder with ##\rho_q##. If i move the cylinder towards ##+\hat{n}##, will it produce a magnetic field? My assumption is that since we have an insulator, then the electrons are bound and there cannot be a current, thus a magnetic field is not produced. Also...

Hello everybody! I want to check out if I've solved correctly: ##\Delta{V}=-E\Delta{x}## ##\dfrac{\Delta{V}}{\Delta{x}}=-E## ##\dfrac{15\;V}{10^{-2}\;m}=-E## ##1,5\times{10^3}\;N/C=-E## ##\vec{E}## direction it's oriented into the XY plane Thanks!

Hello! I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment, as we do with the magnetic and electric energy? Would this require the existence of bodies with negative mass? How could we relate this to the existence or total...

Summary:: What are the prerequisites to study quantum field theory? What are the prerequisites to study quantum field theory?

https://blog.nationalgeographic.org/2014/01/03/dogs-sense-Earth's-magnetic-field/"...the first study showing a mammal not only being able to sense it, but also to exhibit a specific behavior in response to natural magnetic field variations. " In my view, dogs are nearer human consciousness than...

I couldn't solve the question. Can you help me?

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I am trying to understand but without a succes why symmetric magnetic field around ##Z## axis make that ##\hat \phi## magnetic field is zero I can't understand why it physically happens and also how can I derive it mathematically? What does the word symmetric means when talking about magnetic...

I've been reading through this paper to try and get a better understanding of how batteries work. The analysis there is fine (they consider a voltaic cell to charge a capacitor in order to derive ##\Delta V=\varepsilon##, and go via an energy route), but it doesn't really touch upon the fields...

Can we assume that square charge resembles a sphere shell, and think like electric field at sphere shell's center is 0.

Or at least honing ones scientific skill/knowledge? How would one go about this? NOTE: I am talking about a non-pandemic or otherwise non-emergency condition.

I need some advice and help please -Is There a two body force field suitable to study silica crystal or alpha quartz crystal? it's okay to gives Approximate results. - Is the BKS force field suitable for silica crystal? - If there are other simple terms of force field for studying the silica...

There's a constant magnetic field B. If a particle is acted on by a force qv*B (* cross) only, and the initial velocity v0 is normal to B, is the motion certainly a circular one (for any m, q, v0)? mv''=qv*B If one solves this equation (vector), it doesn't seem obvious.

I am sure I need to use Amper's law to do that. if I use the equation I mentioned above it easy to calculate the right side of the equation but I have problem how to calculate the path integral. I know from right hand rule that the magnetic field will point at $$Z$$ and the current is in...

Hi, I would like to ask for a clarification about the difference between parallel transport vs Lie dragging in the following scenario. Take a vector field ##V## defined on spacetime manifold and a curve ##C## on it. The manifold is endowed with the metric connection (I'm aware of it does exist...

Consider the field creation operator ψ†(x) = ∫d3p ap†exp(-ip.x) My understanding is that this operator does not add particles from a particular momentum state. Rather it coherently (in-phase) adds a particle created from |0> expanded as a superposition of momentum eigenstates states...

I have an ordinary switchable magnet for holding tools to a lathe. It's like a magnetic force gearbox, but I can't quite understand the force multiplication. When placed on a steel surface the switch force is approximately ~5N on both finger and thumb at 1.5cm radius acting over a 3cm arc...

Ampere´'s law with the correction term I have a infinite cylinder with radius R with a current density , and magnetic field . I have to proof that it is acceptable to discard the correction term of term of ampere's law, while calculating the magnetic field, as long as it obeys the following...

Summary:: Not sure if my solution to a magnetostatics problem is correct [Mentor Note -- thread moved from the technical forums, so no Homework Template is shown] I was trying to solve problem 2 from...

I derive the quadratic form of Dirac equation as follows $$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$ And I need to find the form of the spin dependent term to get the final expression $$g...

I think the right solution is c). I'll pass on my reasoning to you: R=6\, \textrm{cm}=0'06\, \textrm{m} \sigma =\dfrac{10}{\pi} \, \textrm{nC/m}^2=\dfrac{1\cdot 10^{-8}}{\pi}\, \textrm{C/m}^2 P=0'03\, \textrm{m} P'=10\, \textrm{cm}=0,1\, \textrm{m} Point P: \left. \phi =\oint E\cdot...

Hello, A generic vector field ##\bf {F} (r)## is fully specified over a finite region of space once we know both its divergence and the curl: $$\nabla \times \bf{F}= A$$ $$\nabla \cdot \bf{F}= B$$ where ##B## is a scalar field and ##\bf{A}## is a divergence free vector field. The divergence...

a) \vec{F}=\vec{E}\cdot q \phi =\oint \vec{E}d\vec{S}=\oint \vec{E}d\vec{S}=\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \perp}+\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \parallel}=0+\oint EdS\cdot \underbrace{\cos 0}_1= E2S \dfrac{Q_{enc}}{\varepsilon_0}=\phi \left...

The equation of motion can be integrated w.r.t. ##t## since ##\frac{d}{dt} (\mathbf{r} \times \mathbf{B}) = \dot{\mathbf{r}} \times \mathbf{B} + \mathbf{0}## $$\int (q\dot{\mathbf{r}} \times \mathbf{B} + m\mathbf{g}) dt = \int m\ddot{\mathbf{r}}(t) dt$$ $$\frac{q}{m} \mathbf{r} \times \mathbf{B}...

In this image of Introduction to Electrodynamics by Griffiths . we have calculated the vector potential as ##\mathbf A = \frac{\mu_0 ~n~I}{2}s \hat{\phi}##. I tried taking its curl but didn't get ##\mathbf B = \mu_0~n~I \hat{z}##. In this thread, I have calculated it like this ...