Questions tagged [magnetostatics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
5
votes
1answer
2k views

What is the importance of vector potential not being unique?

For a magnetic field we can have different solutions of its vector potential. What is the physical aspect of this fact? I mean, why the nature allows us not to have an unique vector potential of a ...
9
votes
1answer
4k views

Is Biot-Savart Law valid for time-varying currents unlike Ampere's law?

I have just finished learning the basics of magnetism, and it should be noted that I am not very familiar with Maxwell's equations. Note: In the question, when I say "Ampere's Law", I am referring ...
2
votes
2answers
1k views

Ampère's law applied on a “short” current-carrying wire

Why doesn't Ampère's law hold for short current carrying wires? Of course, such wires should be part of a closed circuit, but that's a physical fact, and there is a numerous amount of ways to close it....
3
votes
3answers
2k views

Direction of electric dipole moment and magnetic dipole moment

For electric dipole: The direction of the dipole moment is from negative to positive charge, but that of the electrostatic field is from positive to negative. But in the case of magnetostatics, the ...
34
votes
4answers
6k views

Why is this vector field curl-free?

The curl in cylindrical coordinates is defined: $$\nabla \times \vec{A}=\left({\frac {1}{\rho }}{\frac {\partial A_{z}}{\partial \varphi }}-{\frac {\partial A_{\varphi }}{\partial z}}\right){\hat {\...
7
votes
1answer
453 views

For a constant magnetic field, is there a gauge with both canonical momenta conserved?

To describe a constant magnetic field $\mathbf B=(0,0,B)$ (ignoring the motion along the $z$ dimension) within hamiltonian (or quantum) mechanics, one needs to choose a gauge. One common gauge is the ...
4
votes
1answer
4k views

Ampere's circuital law for finite current carrying wire

When I was studying about Ampere's circuital law. Then there comes a question in my mind that "whether this law is applicable for finite current carrying wire or not"
5
votes
1answer
1k views

Current geometry and Ampere's law

Under the right circumstances, Ampere's law $\oint \vec H\cdot d\vec \ell=I_{encl}$ can be used to deduce the field $\vec H$ at a point from the current enclosed by the circuit which produces $\vec H$....
2
votes
2answers
1k views

Why is there a magnetic field around a magnet if there are no charges moving? [duplicate]

From what I understand, the magnetic force is just a relativistic effect of the electric force, and I understand how this is can be the case when considering the magnetic field generated by a current- ...
1
vote
2answers
258 views

What causes the pattern you see when you hold a strong magnet near a CRT TV?

When you hold a powerful magnet near an old-style CRT TV, you see an interesting pattern, which "shows up the field lines" (see https://www.youtube.com/watch?v=_yEu2R1gYSs&feature=youtu.be&t=...
5
votes
1answer
188 views

Question about the definition of magnetostatics

From my understanding, magnetostatics is defined to be the regime in which the magnetic field is constant in time. However, Griffiths defines magnetostatics to be the regime in which currents are "...
6
votes
2answers
543 views

What are the possible magnetic fields with constant magnitude?

A now-deleted answer to this recent question prompted me to wonder about this and I can't find a clear answer in the top layer of google results, so I thought I'd ask here. What are the possible ...
3
votes
2answers
3k views

What is the permeability of a permanent magnet?

The following is a diagram that shows the B- and H-fields of a permanent magnet. Inside the magnet, the H-field is in the opposite direction to the B-field, because of the magnetisation M-field and ...
1
vote
1answer
142 views

Current Density In a 3D Loop - Discretising a Model

I'm working on a finite element model as part of a line of research. Specifically I'm consider using vector finite elements (i.e 3 values x,y,z per node) to solve the Poisson equation in magneto-...
5
votes
1answer
866 views

What is the correct expression for the magnetic energy density inside matter?

I'll use a magnetized sphere as an example, of radius $R$, with a magnetization density $\vec{M}$. The magnetic moment of the sphere is $\vec{\mu} = \vec{M} \, V$. The magnetic field inside and ...
4
votes
1answer
333 views

When does $\nabla \times B =0$?

In my lab, I use electromagnets to apply a magnetic gradient force to lots of very small (superparamagnetic) nanoparticles embedded in an elastic medium. I believe that these can be treated as ...
4
votes
2answers
4k views

Ampère's law vs Biot Savart law

So I feel like I understand how both these laws work however it seems like Ampère's law will find the strength of the magnetic field at a point (the point is taken as $z$ in this example and the red ...
1
vote
1answer
652 views

Which surface to use in Ampere's law?

In calculating the current enclosed by an Amperian loop, one must, in general evaluate an integral of the form $$I_\text{encl} = \int \mathbf{J}\cdot\mathrm{d}\mathbf{a}$$ The trouble is, there are ...
0
votes
4answers
5k views

What is the difference between the magnetic field of a permanent magnet, and that of an electromagnet?

What is the difference between the magnetic field of a permanent magnet, and that of an electromagnet? In the diagram below, you can see that the magnetic field of a wire which carries a DC ...
0
votes
2answers
989 views

How to get image current in magnetostatics? (magnetic slab)

I want to know the image current and its location which satisfies the boundary condition at the interface. This problem was originated from the problem 6-33 in Fields and wave electromagnetics, D. ...
-1
votes
1answer
190 views

Why do we consider a circle as a closed loop while deriving the magnetic field of a infinitely long wire [closed]

Why do we consider a circle as a closed loop while deriving the magnetic field of a infinitely long wire. How does it affect if I take another shape.