Questions tagged [magnetostatics]

The study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary.

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Magnehydrotostatic equilibrium

in plasma physics the magnetostatic equilibrium is defined as $$ \vec{j}\times\vec{B}=\nabla p $$ where $\vec{j}$ is the current density $\vec{B}$ is the magnetic field and $p$ is the pressure. But ...
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Can you magnetize iron by putting it in the air cap of a two parallel plates capacitor?

Usually we magnetize iron by putting it inside a solenoid strong homogeneous field and charging/discharging the solenoid several times. I am asking if we can magnetize an iron piece by putting it ...
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Meaning of the Eigenvalues of the Hessian Matrix in Polar Coordinates in a Ferromagnetic System

I have the Hamiltonian for a magnetostatic system (exchange, dipole-dipole, zeeman) which is in polar coordinates since the spins are confined to being in-plane. If I calculate the Hessian Matrix of ...
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Is the vector potential constant in an ideal conductor in magnetostatics?

Suppose we take the Coulomb gauge $\nabla\cdot\mathbf{A}=0$ when defining the vector potential, so that within an ideal conductor, where $\mathbf{E}=0$, and (on physical grounds) we assume $\mathbf{B}=...
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Maxwell Wave Equation intuition [closed]

It is well known that a change on the electric field, will provoke a change on the magnetic field and vice versa. If you (with maths or in real life) change a little bit the electric field, then the ...
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How the force on magnetic charges are introduced with magnetization field?

In the most text books used in Japanese highschools, $H$ field is introduced for magnetic field before $B$ field (flux density) is introduced. The definition in the textbooks is as follow: When a ...
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Griffiths definition of surface current density

I have some questions about how current and surface current density $\mathbf{K}$. Griffiths defines it with the "ribbon" highlighted in black with infinitesimal width $dl_{\perp}$, running ...
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Change in electric field due polarisation in a moving frame

I was deriving the halls effect equation for the case in which there is a moving liquid of velocity v in a under a perpendicular magnetic field. Now what I thought that by force balance $qBv=qE$, but ...
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Divergence of the vector potential in Lorenz gauge, in magnetostatics

If we consider a localized current distribution and the following natural boundary condition : $\vec A(\vec r \rightarrow 0)$ for $\vec r \rightarrow \infty$ If $$\vec A(\vec r)=\int_V G_0(\vec r, \...
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I was solving some Parity Question then, I came across that is magnetic field is parity invariant?

Magnetic field is given by Biot-Savart's Law : $$\vec{dB} = \frac{\mu_o}{4\pi}\int \frac{I (\vec{dl}\times \hat r)}{r^2}$$ If $P$ denotes the Parity Operator then : $$P :B\to \,\,\, ?$$
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How to explain attraction or repulsion of two current coil in terms of energy

We know current (dc) carrying loop can be thought of a magnet . And two current carrying loop (placed closely) will attract or repel each other depending on orientation of coil and direction of ...
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What is the field of a magnetic dipole near a conducting sphere?

Suppose I have a perfectly conducting sphere in vacuum, and I place a magnetic dipole near this sphere. Simply stated, the magnetic field of the dipole will be distorted by the presence of the ...
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Conservative magneto-static field on a current carrying wire?

$$\nabla \times \mathbf{B}=0$$ I am asking why although magneto-static $B$ fields in total are considered as non-conservative fields by most of the literature, the magnetic field of a d.c. current ...
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Derivation of the force between two current loops [duplicate]

Could you explain me how to derive the force between two current loops carrying currents $I_1$ and $I_2$, written as a double loop integral: $$ \vec{F}_2 = \frac{\mu_0}{4 \pi} \oint \oint \frac{I_2 ...
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Examples of current densities

I am trying to imagine how do the continuous current density look like. When we speak about charge density, if it is discrete, one can picture multiple point charges in a region in space. If the ...
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Further uncertainties in magnetostatic

In magnetostatic, the continuity equation is as follows: $$\frac {\partial\rho(\vec r,t)}{\partial t} + \nabla \vec j(\vec r,t)=0$$ In magnetostatic $\frac {\partial\rho(\vec r,t)}{\partial t}=0$ and ...
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Uncertainties in magnetostatic

Today in our lecture we were introduced to Magnetostatics. While I was able to understand mathematically and physically the majority of the new things that were mentioned, there are a couple of things ...
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Is magnetic moment a conserved quantity in Magnetostatics?

I am interested in the equations of Magnetostatics, but without the knowledge that electric currents create magnetic fields. In other words, expressing the equations only in terms of the magnetic ...
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Ampere's Law and 3th Newton's Law

In the textbooks of REITZ/MILFORD/CHRISTY(Fundaments...) or WANGNESS(Eletromagnetic fields)it is said that Ampere’s Law breaks 'aparently’ the 3ª Newton’s Law. Wangness explains in this way: Ampere’...
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$\nabla \cdot J = 0$ Why is amperes law only valid for non time varying currents

Taking the divergence of amperes law gives $\nabla \cdot J = 0$ Comparing this to the continuity equation, amperes law requires that for it to be valid $ \partial \rho / \partial t = 0$ Meaning that ...
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How in Faraday rotator, changing magnetic field will change the refractive index of RCP and LCP?

Can anyone mathematically prove how in the faraday rotator, when we change the magnetic field direction, it will change the refractive index of Right circularly polarized (RCP) and Left circularly ...
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Suspension of magnet with a thread

Recently, I have read about magnetic poles of Jupiter. Peculiar thing is, that Jupiter has 3 magnetic poles. If you would suspend a magnet via thread on earth, it would align itself in geographic ...
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Validating Basic Laws of Magnetostatics [closed]

I am having trouble with the following problem, although with similar problems I run into the same issue when it comes to validation. The example problem below is a problem for Amperes Law. The ...
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Vector potential of a square loop [closed]

I am doing my homework and I'm really stuck on this problem. It asks for the magnetic field due to a square, lying in the $xy$-plane, of side lenght $a$ and with a electric current $I$ running ...
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Force Between Solenoids (Without Magnetic Charge!)

I'm designing a system in which two (air-core) solenoids on the same axis are used to produce an elastic, contactless collision on a track through their opposing magnetic fields. I understand that ...
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Electric current density when electric charge density is null?

I was reviewing electrodynamics then some minor detail caught my attention. In the notes I am reading (David Tong's), it has electric charge density $\rho=0$ but at the same time it assumes a steady ...
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Magnetic field due to a finite-length straight wire carrying a constant current

My question: I want to find an expression at any point in space for the magnetic field $\mathbf B$ produced by a straight wire of finite length $L$ carrying a constant current $I$. I think that we can ...
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Magnetic field of a cylinder surrounded by another cylinder

I made an experiment for a school presentation where I have to measure the magnetic field in the space arround a circular cylinder of cross section $S = \pi r^2$ through which passes a uniform current ...
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Interpretation of Poynting Vector

Short Version How exaclty can the Poynting vector be physically interpreted for static electric and magnetic fields? I know that it describes the magnitude and direction of energy flow in EM-waves. ...
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Are the field lines on a bar magnet diagram contour lines?

Following is the representation of magnetic field lines around a bar magnet. The lines drawn, indicate the direction of magnetic field lines. Now I want to know that is this a contour mapping of the ...
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What effect do two perpendicular magnetic fields have?

What is the effect of 2 perpendicular magnetic fields? My teacher discussed this illustration in class where there were 2 perpendicular magnetic fields. He said that they both cancel each other out. I ...
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Is the current density constant in magnetostatics?

I'm thinking about the conditions needed for magnetostatics, in other words magnetic fields that do not change with time. My textbook says that this requires a steady, continuous current without any ...
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Magnetostatic: integral form of magnetic torque of a hard ferromagnet in an external magnetic field

It seems very easy but I can't find the expression of a magnet of magnetization (magnetic moment density) $\vec{M}$ in an external field $\vec{B}$. I found in the Jackson Classical Electrodynamics the ...
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Are electrostatic and magnetostatic fields quantised?

Most things in fundamental physics come quantised. There is even a hunt for the hypothesised quantum of gravity, the graviton. Magnetic fields are quantised under certain specific circumstances, such ...
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Ampere's Law in infinitely permeable materials

Consider an infinitely long wire carrying a continous current $\mathbf{I}$. It is surrounded at some distance by a hollow cylinder of infinite permeability $\mu$ and zero conductivity (i.e. it can't ...
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Magnetic field in two conducting parallel plates. (stripline) [closed]

Studying Poynting Vector power density I found a geometry that I really can't figure it out and is nowhere to be found on the internet. I have two conducting parallel plates with opposite surface ...
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Is it perpendicular each other between r component vector and $\theta$ component vector of the magnetic field vector?

Currently I'm very new to static magnetic field. Cited from here As I see many diagrams of magnetic field, I found that each $H_{\theta}$ and $H_{r}$ are seemingly perpendicular each other. Is it ...
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A confusing problem in electro- and/or magnetostatics: two parallel cylinders with opposite currents

I got the following problem as a part of my assignment in physics: Equal but opposite currents $J$ flow on the surfaces of two cylinders of radii $R_1$ and $R_2$, respectively, with the axes of the ...
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Question about current from moving line charge in Griffiths' Electrodynamics

On page 217 of the 2013 version of Griffiths' Electrodynamics textbook, he says "A line charge $\lambda$ traveling down a wire at speed $v$ constitutes a current".$\lambda$ traveling down a ...
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Factor before Dirac delta in magnetic dipole field formula

I bumped into this formula for the magnetic induction field generated by a dipole, containing Dirac's delta, while studying hyperfine splitting: $$\textbf{B}(\textbf{r}) = \frac{2}{3}\mu_0 \textbf{m}\...
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Surface Current Density

I'm trying to derive the boundary conditions for magnetic field and if I try to derive the condition for the tangential component of magnetic field. From the figure and Maxwell's law for line ...
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Magnetostatics and Newton's third law

Here's a simple question that has been driving me to distraction. Having issues uploading images, so I'm just going to have to describe the system. Let's say we have a solenoid oriented along the $z$...
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2 votes
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Confused about the notion of steady current

One of the textbooks I’m reading states that an electric current is said to be steady if $\nabla \cdot \mathbf J = 0$, which is equivalent to $\frac{\partial \rho}{\partial t} = 0$ by the continuity ...
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Why should there be an induced electric field if magnetic field is constant? [closed]

Problem statement: The curved surface of a very long hollow non conducting cylinder of radius $R$ is uniformly charged with surface charge density $\sigma$. A non conducting small circular ring of ...
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Where does one more '$\rm m$' come from in the units?

$$\nabla \times A = B$$ $A$ is vector magnetic potential, $\mathrm{Wb/m}$ $B$ is magnetic field intensity, $\mathrm{Wb/m^2}$ Where does one more m come from for $B$? Is that from the gradient operator ...
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How to find magnetic field as a function of $r$ from axis of solenoid?

I was solving this problem: Whose answer is given as: I understand the part for calculating the field outside the cylinder, but for inside, I don't get it. If we apply Ampère's circuital law by ...
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Relation between quasi-static and fully dynamic $\vec E$ and $\vec H$

Imagine an infinitely long coaxial cable with an inner wire of radius $a$ and outer radius $b$. The space in between the cable is filled with air ($\epsilon=\epsilon_0$). Suppose the inner cable ...
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What carries the electrostatic and magnetostatic forces?

In the Standard Model of QM, all forces are mediated or carried by particles (for want of a better word) called bosons. The photon is an example of a force-carrying gauge boson, and mediates the ...
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Solving Laplace's Equation for magnetostatic problem in the absence of currents

I am attempting to simulate the resulting magnetic field distortion of paramagnetic nanoparticles in a static magnetic field in the absence of currents, in 3D. In my system, the static magnetic field ...
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What is the formal definition of $dI$? Where $I$ stands for current?

Two days before my magnetostatics test and for some reason the idea of current just stopped making sense. I think I pin pointed the problem to $K$ and $J$, the so called surface and volume current ...
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