# What is Magnetic potential: Definition and 30 Discussions

Magnetic vector potential, A, is the vector quantity in classical electromagnetism defined so that its curl is equal to the magnetic field:

×

A

=

B

{\textstyle \nabla \times \mathbf {A} =\mathbf {B} \,}
. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.
Vector magnetic potential was first introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively. Lord Kelvin also introduced vector potential in 1847, along with the formula relating it to the magnetic field.

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1. ### A Relationship between magnetic potential and current density in Maxwell

I am currently studying to solve Maxwell's equations using FEM. I have a question about Maxwell's equations while studying. I understood that the magnetic potential becomes ▽^2 Az = -mu_0 Jz when the current flows only in the z-axis. I also understood the effect of the current flowing in a...
2. ### I Is the scalar magnetic Potential the sum of #V_{in}# and ##V_{out}##

Hi, I'm wondering if I have an expression for the scalar magnetic potential (V_in) and (V_out) inside and outside a magnetic cylinder and the potential is continue everywhere, which mean ##V^1 - V^2 = 0## at the boundary. Does it means that ##V^1 - V^2 = V_{in} - V_{out} = 0## ?
3. ### A Solving Laplace's equation in polar coordinates for specific boundary conditions

Hello everybody, Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
4. ### What is the origin of magnetic potential energy?

Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B: $$U=-\boldsymbol{\mu} \cdot \textbf{B}$$. However, I was told that magnetic fields are non-conservative, so we can't...
5. ### Calculate magnetic potential of a given current density

Hello, I'm current studying magnetostatics and I'm struggling to understand the equation for A. Here is the equation from Griffith in the attachment. My confusion is, if the object is a cylinder and the current density is a function of s, J(s), then how would I write r-r'? Thank you!
6. ### What is the vector magnetic potential for a rod extending along the Z-axis?

I am trying to calculate the vector magnetic potential for a rod of length L extending along the Z-axis. I was asked to find the magnetic potential at a point P which is a distance r from the center of the rod in the XY plane. I know the formula I have to use is the vector Poisson's equation A...
7. ### Second derivatives of magnetic potential

Hi there! It looks like you are trying to prove that the second derivatives of the magnetic potential function ##\mathbf{A}## belong to the class ##C(\mathbb{R}^3)##. This is a great question and involves some advanced mathematical techniques. One approach you can take is to use the dominated...
8. ### 2 Types Of Magnetic Potential Energy

There are 2 types of magnetic potential energy equations: 1. ##U = -\vec \mu \cdot \vec B## 2. ##U = \frac{1}{2} \int \mathbf{A} \cdot \mathbf{J} \, \mathrm{d}V## - I have searched for the second equation, only can find some information in one web site. Do you know what their names are and...
9. ### Magnetic Potential & Magnetic Field

Homework Statement I'm given an infinite cylinder with radius a. There's a uniformal current density j flowing in the cylinder in the z direction. I'm asked to find the magnetic field in the following ways -Ampere's law -Magnetic potential and then use it to calculate the magnetic field. The...
10. ### How Do Scalar Magnetic Potentials Relate to Cylindrical Fields?

Hello, I'm really stuck, I don't know how to start ! Homework Statement In the regions where Jl=0, we have ∇x H=0, so we can introduce a magnetic scalar potential Vm such as H=-∇Vm. A long cylinder of radius R of linear magnetic material of permeability μr. The cylinder axis is in z...
11. ### Center of magnetic potential vs center of mass

first i might be using magnetic potential incorrectly so please be nice when correcting me. i'm attempting to model the behavior of a magnetic compass when it is placed next to a ferrous piece of metal. basically the compass will point to the metal rather than north. my first simplification...
12. ### Vector B in Magnetic Potential Energy

U = -m x B Is B the total magnetic field of the whole system? If there is two objects X,Z and they all have a magnetic field. But different strengths, I want to calculate the U for Z, B should be the total magnetic field of BOTH fields or only X's field strength? Since X is the...
13. ### The Curl of Magnetic Potential

Hi guys! I recently saw on Wiki that given a magnetic potential A(r)=(u/4π)(mXR/r^3) ,( where u is the permeability of free space, m is the magnetic dipole moment of a magnetic field, R is the position vector, and r is the distance from the magnetic field ) upon taking the curl of the magnetic...
14. ### What is magnetic potential energy?

We know that a Magnetic field does no work. Then how does an inductor store energy (1/2 LI2)? When that stored energy is needed, it can be retrieved back and clearly it can be used to do some work. In a fix here.
15. ### What Is the Role of the Second Term in Magnetic Energy Functional Analysis?

Dear all, I'm reading a paper on finite element magnetic field analysis. Basically there are two approaches to this. One is to use Maxwell equation and the other is to define an energy functional, discretize the problem and minimize the functional with respect to the unknowns. The paper takes...
16. ### Gauge Freedom of Magnetic Potential in Electrodynamics

Hi, In Electrodynamics, one often state about the gauge freedom of the magnetic potential. And so, we may choose to impose for example the Coulomb gauge, where the divergence of the potential is zero. But, isn't this only true if there exist no changing electrical field, \frac{\partial...
17. ### Obvious Magnetic potential question

Homework Statement I've been given a scalar magnetic potential of \phi = D cos (\theta) and asked to prove that this corresponds to a constant magnetic field. It's obvious that it does but I keep running into walls! Homework Equations \bar{H} = - \nabla \phi \bar{H} = -D cos...
18. ### How to Set Lower Limit for Intergration on Vector Magnetic Potential Problem

Homework Statement My question is mainly on the set up of the limits of the integral. The original question is: Find vector magnetic potential A distance s from a infinite long straight wire carrying DC current I. The Attempt at a Solution Let wire on z-axis and \vec I =...
19. ### How to find vector magnetic potential given magnetic field?

If we are given B, how can we find A? I can fine the magnitude of A by: \int_{s'} \vec B \cdot d\vec{s'} = \int_{s'} (\nabla X \vec A) \cdot d\vec{s'} = \int_{C} \vec A \cdot d\vec{l} So given B and the surface area, you can get the magnitude of A. But how do you get the direction...
20. ### Semiclassical Bohr quantization with a magnetic potential

Homework Statement given the Hamiltonian in one dimension H= \frac{(p-eA)^{2}}{2m}+ V(x) use the Bohr-Sommerfeld quantization in one dimension to obtain n=n(E) Homework Equations Hamiltonian , quantization The Attempt at a Solution from the usual quantization algorithm in one dimension i...
21. ### Gravitational / Magnetic Potential Energy Question

To get energy out of an object falling down to Earth or a magnet slamming into another one, you have to lift the object up or pull the one magnet away from the other, which makes sense with Newton's laws. I was wondering, if an object just "magically" appeared out of nowhere in the air...
22. ### Magnetic potential derivation from B

π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô Homework Statement Derive the vector potential A produced by an infinite straight wire of negligible thickness, located in free space and carrying a static electric current I. Homework Equations The Attempt at...
23. ### Vector magnetic potential of current sheet

Hi. Say I have an infinite sheet of current. My book gives the following formula for the vector magnetic potential \mathbf A=\frac{\mu_0}{4\pi}\int_{V'}\frac{\mathbf J}{R}dv' But when I do the integral, it doesn't converge. However, if I calculate \nabla\times\mathbf A, i.e. move the...
24. ### Why Is My Calculation of Magnetic Potential Energy Incorrect?

Homework Statement Homework Equations U = -\vec \mu \cdot \vec B The Attempt at a Solution As you can see, I calculated \mu = 4.08x10-3 and got the torque on the loop which is shown in the answer above. The potential energy is defined above as U = -\vec \mu \cdot \vec B =...
25. ### Computing Hr and Hz from Magnetic potential

Hello everybody, My question to you is how can I compute the values of Hr and Hz given the value of A - the magnetic vector potential. The reason I seek this: I'm using the FEMM software to obtain the H values at points around a solenoid. The .ans file that FEMM creates has a huge list of...
26. ### Magnetic Potential of Long Straight Wire: 65 Chars

A long straight wire of radius R carries a unifrom current density \mathbf{J} inside it. In the first part of the question I worked out that the magnetic field inside the wire was \mathbf{B}=\frac{\mu_0 I r}{2 \pi R^2} \mathbf{\hat{\phi}} I am now asked to get the vector potential insde...
27. ### Magnetic Potential: Computing the Curl of $\mathbf{A}$

hi again, I'm trying to show that \mathbf{B} = \nabla \times \mathbf{A} where \mathbf{A} is the magnetic potential given by: \mathbf{A(r)}=\frac{\mu_0}{4 \pi} \int dV' \frac{\mathbf{J(r')}}{|\mathbf{r-r'}|} i deduced that since...
28. ### Magnetic Vector Potential Around a Wire Carrying Current

Until about ten minutes ago I had never heard of the magnetic vector potential \vec A , defined such that \vec B = \nabla \times \vec A . I am having trouble visualizing this. What would the magnetic vector potential field look like around a straight wire carrying a (constant) electric...
29. ### Why magnetic potential on a moving charge=q v.A ?

Hi, Can ny one direct me to a reference that explains in detail that the magnetic potential on a moving charge = q v.A or at least why is the generalized force on a charge in a velocity dependent potential(U) in terms of the generalized coordinates: Fj = - dU/dqj+d/dt (dU/dvj) ? vj is the...
30. ### Magnetic potential and inverse square law

Hi I am in doubt about the lack of the squared distance r in the expression below: v(r)= constant* int_vol div M /|r_0 - r| dV M: magnetization vector r : displacement vectors Is it correct to say that magnetic potential V(r) obeys the inverse square law ? Or it is more correct to say that...