Vector potential Definition and 164 Threads

Homework Statement For the magnetic field B=k/s3 z determine the magnetic vector potential A. For simplicity, assume that A does not have a component in the s direction. (I don't know if this is relevant but this was a follow up question to one in which I was required to find the...

Special relativity predicts that electric fields transform into magnetic fields via Lorentz transformations and that the vice versa also occurs. It also has been argued, since experiments verifying the quantum mechanical phenomenon of the Aharonov–Bohm effect, that the vector potentials are more...

Suppose my reference system is x coming out of the page toward you, y is in the plane of the page going left and right and z is in the plane of the page going up and down. Further suppose that the magnetic field is parallel to the x-axis and the electric field is parallel to the z axis. Finally...

I have some trouble with the calculation of energy in magnetostatics, using the vector potential A. From the classic formula that uses B*H, I find the expression (in magnetostatics) in terms of A and J (current density): \begin{align}W &=\frac{1}{2}\int_V{\vec{B}\cdot\vec{H}{\rm d}V}\\...

In problem of finding the vector potential of a vector F = yz i + xz k + xy j, the solution gives in Griffith's solution manual is http://img843.imageshack.us/img843/2725/vectorpotential.jpg Uploaded with ImageShack.us But I don't understand how we can integrate \frac{\partial Az}{\partial...

Homework Statement The concept of a scalar potential is reasonably straight forward. It is the energy needed to move to a point from some arbitrary reference point, the reference point being the origin for most mechanical problems and infinity for most electromagnetic problems.And of course...

Homework Statement There is a cylinder of conducting ionized gas that occupies rho < a. For the given B, show that a suitable A can be found with only one non-zero component, Aphi, find Aphi which is also continuous at rho=a. (Part A was solving for a few relavant things) Homework Equations...

Hi, The vector potential for elctrodynamics, A_{\mu}, can be decomposed A_{\mu}\in\mathbf{0}\oplus\mathbf{1} but the \mathbf{0} part we ignore. My question is: do we ignore the scalar part because of experiment, or is it ignored for mathematical reasons I am naive about? Thanks,

The Aharonov-Bohm effects show how a electro-magnetic field could affect a region of space in which the field had been shielded, although its vector potential did exist there and could interact with the wave function of say the electron. What practical application(s) (so far) can be derived...

hi everybody i want to solve the wave equation of the magnetic vector potential numerically in x-y plane grid, curl curl A= µ J anyone can help me thanks in advance

Hi there, during my work on my PhD thesis as an experimental physicist I ended up with a very theoretical problem: What does the wavefunction of an electron traveling through a magnetic vector potential look like? I chose a cylindrical coordinate system with a magnetic vector potential A...

Hi all, I was reading the http://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#Electromagnetic_field_and_vector_potential" and I am a little bit confused. In this equation defining the vector potential \mathbf{A}(\mathbf{r}, t) = \sum_\mathbf{k}\sum_{\mu=-1,1} \left(...

I was reading the text of electricity and magnetism by griffiths. Here I read a term called magnetic potential but I did not completely understood the physical essence of the term, neither it is explained in the book. It should have some physical interpretation as it is named a potential. In...

Homework Statement An infinite sheet of copper conductor, thickness t, lies in the xz-plane. The sides of the sheet intersect the y-axis at y=\pm\frac{t}{2}. The current density in the sheet is given by: {\bf{j}}({\bf{r}}) = \begin{cases} j_0\left(\frac{y}{t}\right)^2{\bf{\hat{x}}}, &...

Hi I am studying magnetic vector potential from Griffiths book. The eq 5.76 in his book gives the boundary condition for the magnetic vector potential. \frac{\partial \vec{A_2} }{\partial n}- \frac{\partial \vec{A_1} }{\partial n}=-\mu_o \vec{K} where n is the vector perpendicular to the...

Hi, I would like to verify analytically that a vector potential of the form A=1/2(-yB0,xB0,0) produces a constant magnetic flux density of magnitude B0 in the z direction. (I guess I'd have to use the relation B=\forall\wedgeA...)

This is not my theory, or even new, rather pertaining to established physical knowledge, but I simply find it fascinating. It pertains to several areas of physics, and/or variational mathematics, so I've posted it here in the General Physics area. My reasons for posting is because it is one...

Greetings everyone, I have been reading up on the magnetic vector potential, and I understand the vector calculus behind its definition and use. However, I am seeking an intuitive way to understand what it is conceptually, not just mathematically. I am assuming that any conceptual...

Hi everybody! I'd like to understand the physical meaning of the Feynman's vector potential definition: $ A_{m}^{(b)}(x) = e_b \int \delta (xb_{\mu}xb^{\mu})db_m(b), \qquad m=0,1,2,3 $ (component m of the vector potential of the particle b at the point x) Here - the integration is done over...

Has vector potential in classical electrodynamics a physical reality or it's just a mathematical tool?

Homework Statement What current density would produce the vector potential A(r)=(-kmu/2pi)In(r/a) (in the z direction) where k is a constant, in cylindrical coordinates? Homework Equations The Attempt at a Solution i have done this three times and i get zero current...

\vec{B}=rot\vec{A} \vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi If I define \varphi=\widetilde{\varphi}-\frac{\partial f}{\partial t} \vec{A}=\widetilde{\vec{A}}+gradf where f=f(x,y,z,t) I will get \vec{B}=rot\vec{A}=rot\vec{\widetilde{\vec{A}}}...

Anyone know of a Lagrangian given in terms of E and B (or equivalently the tensor F) that yields Maxwell equations? A link or reference would be appreciated. I can write down such a Lagrangian which yields the two second-order Maxwell equations, but not the usual four 1st order equations...

Are potentials appearing in the Maxwell equations the components of a contravariant vector or a covariant vector? Let us be specific. metric is (+,-,-,-) . Let us write the potentials which appear in the Maxwell equations as \Phi and \vec{A}=(A_x,A_y,A_z) Is it then the case that...

Homework Statement Give an expression for the magnetic field and show that a magnetic vector exists such as \vec{A}(P) = A(r)\hat{z} and \vec{B}(P) = \vec{\nabla} \times \vec{A} For the infinite wire shown in figure 1. Here is a link to the figure and problem statement. The problem is the...

Let me preface by saying that I am a freshman in an introductory level Electricity and Magnetism course. My professor has assigned this problem, as he briefly introduced the idea of vector potentials, along with curl and divergence operators. I am VERY much lacking in knowledge of any of these...

we know that vector potential in a resonator satisfies the equation \intA(\lambda)A^{*}(\lambda^{'})dV=4\pic^{2}\delta_{\lambda\lambda^{'} So how about in cavity of arbitrary shape? Does this equation still valid? Thanks!

Homework Statement Calculate the magnetic vector potential A at a point p located at a distance r from the axis of an oscillating dipole of length s. It is assumed that r\gg s and that the current is the same throughout s. Homework Equations r=\sqrt{(x^2+(z-z')^2)}, where x,z is the...

Hello! Can you tell me the sufficient condition for the existence of the vector potential? Thank you very much!

Hi, I have a problem involving the Hamiltonian of a particle of mass m, charge q, position r, momentum p, in an external field defined by vector potential A and scalar potential X. Here's the Hamiltonian: H(r,p) = (1/2m)[p - qA(r,t)]2 + qX(r,t) = (1/2m)(pjpj - 2qpjAj + q2AjAj) + qX The...

How can you argue, by symmetry, that the vector potential inside a solenoid depends only on \rho, the perpendicular distance from the axis of the solenoid? And how can you argue that there is only a \hat{\phi} (azimuthal) component of the vector potential, such that \vec{A} takes the form...

I have a field ,B, I need to find the other field,A, such that -> __ -> B = \/ x A I need numerical solution, given B sampled on a 3D computational grid (finite difference hexahedra) find A. What numerical methods could be used?

urgent EMM question Homework Statement find the vector potential a distance s from an infinite straight wire carrying current I, check that dell dot A=0 and dellxA=B... ok i know the answer is A=A(s) z, in cylindricals. A(s)=(mu*I/2*pi)ln(s/a)z when a is a constant. can someone please...

While I understand the mathematical definition of the magnetic vector potential field A ( \bf {B} = \nabla \times \bf {A} ), I don't have an intuitive grasp of its physical meaning. For the (scalar) electric potential the matter seems rather simple. The dimensions of φ are energy per unit...

Homework Statement Find the vector potential \vec{A}(x,0,0) (i.e. on the x-axis) for a current loop of radius a, carrying a current I in the \phi direction. Homework Equations \vec{A} = \frac{\mu_0}{4\pi}\int_{V'}{\frac{\vec{J}dV'}{R}} Where R is the distance from the source point to the...

The vector potential can be expressed in the following way: ∇^2 Ay-∂/∂y (∇∙A)=-μJy (Here only taking y components) Vector A is not determined uniquely. We may add derivatives of an arbitrary function (gradient) to the components of A, and the magnetic field does not change (curl of...

Why is it that I can't find a drawing on the internet of what the magnetic vector potential looks like around a current carrying wire?

In David Bohm's "Quantum Theory" (an intro topic building up to the Rayleigh-Jeans law), he states: "We now show that in empty space the choice div a = 0 also leads to \phi = 0 ... But since div a = 0, we obtain \nabla^2\phi = 0 This is, however, simply Laplace's equation. It is...

Homework Statement Consider a finite wire which lies on the z-axis and extends from the point z=-Λ to the point z=+Λ. The vector potential in the xy plane a distance s from the wire is: Λ->∞ A=(µₒI/2π) ln (2Λ/s) k̂ An equally good vector potential is given by A'=A+∆λ, where λ is any...

Homework Statement There is a disc with radius R which has a uniformly-distributed total charge Q, rotating with a constant angular velocity w. (a) in a coordinate system arranged so that the disc lies in the xy plane with its center at the origin, and so that the angular momentum point in...

http://en.wikipedia.org/wiki/Vector_potential The Wikipedia article is mentioning an interesting formula for defining vector potentials. Isn't that the same thing as a formula \nabla\times\int d^3y\;(V(y)\times\nabla)\frac{1}{\|x-y\|} = -4\pi V(x), where V:\mathbb{R}^3\to\mathbb{R}^3 is...

Hello all. I am hoping someone could lend a hand. I need to determine the vector potential of a long wire. I am given the B-field = (\muI)/(2\pir) and I know at some point I will need to use \nabla X A. Thanks in advance.

Prove that 4 vector potential does really a 4 vector? Most of the textbooks I found only mention that divergence of 4 vector potential equals to zero and the d'Alembertian of it is a four vector current and therefore it 'should be' a four vector. However I do not see there is any tensor theorem...

em Homework Statement In a certain region, the magnetic field as a linear function of time is given by B = Bo \frac{t}{/tau} z hat Bo and tau constants. A)FInd a simple expression for the vector potential which will yield this field. B)Assuming the scalar potential is a constant, find E...

I'm trying to get from the magnetic vector potential \vec{A}(\vec{x},t) = \frac{1}{\sqrt{\mathcal{V}}}\sum_{\vec{k},\alpha=1,2}(c_{\vec{k}\alpha}(t) \vec{u}_{\vec{k}\alpha}(\vec{x}) + c.c.) where c_{\vec{k}\alpha}(t) = c_{\vec{k}\alpha}(0) e^{-i\omega_{\vec{k}\alpha}t}...

Homework Statement It's problem 2.b) on this page: http://www.phys.washington.edu/users/schick/322A/322-08ps3.pdf The Attempt at a Solution So, what it looks like to me, since the only terms in the actual vector potential are all multiplied, Lambda would have to be a constant, so...

Why is the magnetic vector potential of a point inside a infinite soleniod azimuthal assuming the axis of solenoid is the z axis. Problem is the formulae A(\vec r)=\int_{v} \frac {\vec J(\vec r^{'})}{r} d\tau doesn't hold any more due to the infinite extent of the current

Homework Statement A particle of charge q in a vector potential \vec{A} = (B/2) (-y\vec{i} + x\vec{j} ) show that a classical particle in this potential will move in circles at an angular frequency \omega_0 = qB/ \mu c, \mu is the mass of the particle. Homework Equations The Attempt...

i am having trouble visualiszing what vector potential A means physically. I understand that if you take the curl of it it give you the magnetic field B. I was wondering if anybody could also direct me to a website or show me a proof of how the electric field E is equal to the partial derivative...

can anyone show me how to prove that the partial derivaive of vector potential A with respect t is equal to the electric field E?