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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How to interpret Magnetic Susceptibility as the ratio of two vectors $M$ and $H$, as division of two vectors is not defined in mathematics?
Magnetic Susceptibility, denoted as χ is defined as a scalar, represents the ratio between the Magnetization vector ($\vec {M}$) and the Magnetic field strength vector ($\vec{H}$).
However, in ...
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If the conductor floats in a horizontal homogeneous magnetic field, what is the current?
If the conductor floats in a horizontal homogeneous magnetic field, its magnetic flux density is 0.75 T and one meter of conductor weighs 2.5 g. How to calculate current. So when the length or mass is ...
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Which electromagnetic coil would have a stronger magnetic field, High amperage low voltage or low amperage high voltage?
My apologies if the question is just too simplistic, I asked to ChatGPT and it said that the high amp low volt coil would be the strongest, I just want to confirm.
Assuming that both have the same ...
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Still can't see why $\nabla \times \mathbf J(\mathbf r') = 0$ in Biot-Savart derivation
When deriving the differential form of Biot-Savart's law (which is also Ampere's law under magnetostatic conditions) there is one step which I am still not fully convinced.
We will firstly use this ...
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Computation of surface bound current: ambiguity in the choice of a normal unit vector for a surface
Let us suppose to have two coaxial cylindrical tubes, namely two cylindrical surfaces $\Sigma_1, \Sigma_2$, with a radius of $a$ and $b$ respectively. A current $I$ flows across the surfaces but in ...
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Force on infinitesimal loop as stated in Griffiths' Electrodynamics
I've found little to no success in finding a proof of result given by Griffiths at the start of the chapter on Magnetic fields in matter, namely the one for the force acting on an infinitesimal loop ...
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Force on a circular loop formulae in Griffiths' Electrodynamics
I'd like to ask for some clarifications on the formulas for the force on a loop with magnetic dipole moment immersed in a non-uniform magnetic field, given by Griffiths in Introduction to ...
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Torque on a current loop in a uniform magnetic field
I'm trying to prove the result the net torque on a current loop in a uniform magnetic field is $\vec{\tau}_{net}=\vec{\mu}\times \vec{B}$ where $\vec{\mu}=I\frac{1}{2}\oint(\vec{r}\times d\vec{r})$ ...
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Derivation of discontinuity of vector potential
I'm trying to prove the equation from Griffiths' Introduction to Electrodynamics which tells us that the vector potential ${\bf A}$ is continuous across any boundary (both tangential and normal ...
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Magnetostatics: Boundary conditions
I'm reading chapter 5.4.2 of Griffiths' Introduction to Electrodynamics, and I'm having trouble understanding some of the reasoning and some of the results he obtains.
He starts by considering a ...
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Point dipole approximation limit
Can I approximate the field of a 10 mm length x 5 mm radius cylindrical magnet at 8 mm away using a point dipole approximation?
I was wondering if it would still be possible to create a semi-accurate ...
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Metals and Magnets
A metal is attracted by a magnet when placed in it's vicinity. I was wondering if it is the metal that moves towards the magnet, or is it that both the metal and magnet move towards each other? Could ...
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How can magnetic materials be practically represented in magnetic vector potential?
The magnetic field can be represented in terms of the $H$ field and the magnetization field, often with the magnetization field condensed into the relative permeability constant $\mu_r$ by assuming it ...
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Magnetic field outside of permanent magnet - What is $\vec H$?
If a cylindrical magnet has a uniform magnetization $\vec{M}$ along its axis its magnetic field $\vec{B}$ looks approximately like this:
There seems to be a contradiction to me. Since there are no ...
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Biot-Savart integral over a half-ellipse does not seem to approach the result on the line
I am trying to compute a Biot-Savart integral of the vector potential over one-half of an elliptic path, however as a check I compared the result when the ellipse becomes "squashed" as an ...
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Does this basic example of two bar magnets preserve angular momentum conservation?
Let's say I hold two bar magnets side by side both vertically aligned ($z$-axis). I don't want to worry about their shapes, so let's approximate them as dipoles. I will use the dipole formula rather ...
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Ampere's law on infinite path
I was calculating the magnetic field of a circular current loop using Biot-Savart law and obtained it straightforwardly. If the loop is in the $xy-$plane, centered at the origin, the field at a point ...
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Confusion on Griffith's Electrodynamics Example 5.3
In the fourth edition of Introduction to Electrodynamics, a scenario is described in example 5.3 where a rectangular loop of wire supporting a mass $m$ hangs vertically with one end in a uniform ...
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Enforcing Mathematical Continuity for a System Containing Discontinuity
I am attempting to numerically solve a BVP for a solid core solenoid field. I am starting with:
$\vec{\nabla{}^2}\vec{A_r}=0$
$\vec{\nabla{}^2}\vec{A_\phi}=\frac{\mu}{\mu_0}\vec{J_\phi}$
$\vec{\nabla{}...
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Magnetization Enhancement Using Various Materials
I was looking online at how inserting a material inside a solenoid can enhance/reduce the magnitude of a magnetic field in all space depending on what material is inserted. This makes sense from a ...
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Computing mutual inductance given only magnetic fields
I am experimenting with numerically computing the mutual inductance between a number of coils in the presence of various magnetic materials.
Traditionally, the mutual inductance is found by ...
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Magnetic flux in a loop from a circular coil
Problem
At the center of a circular coil with length $L$, radius $b$ and $N$ windings is there a small circular ring with radius $a << b$. The ring is coaxial with the axis of the circular coil....
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Not understanding Ampere's law
Suppose we have some wire of length $2b$ with a current $I$ flowing through it and we want to evaluate the field at some distance $a$ radially outwards from the centre of the wire (so a distance b ...
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Magnetic field inside a spherical shell with "uniform" surface current
I want to compute the magnetic field on any point $\mathbf{r}$ inside a spherical shell whose surface holds some uniform current that goes circularly around an axis. If the rotation axis corresponded ...
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Conservation of Momentum violation with Lorentz Force
Note: I am describing this question using cylindrical coordinates $\hat{r}$, $\hat{\theta}$, $\hat{z}$.
I've been looking into how you could slow down a plasma moving downstream in a pipe using ...
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Pressing force of a solenoid
If a current is passed through bundle of loosely coiled, insulated wire the space between the wires rapidly contracts, crushing it down into a disk. How can this crushing force be calculated?
I know ...
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Can we use Ampere's law without requiring help from Biot-Savart law?
Consider the case of a straight, infinite wire carrying uniform current. From reversing the direction of the current we can rule out radial dependence of the magnetic field but are left with two ...
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Magnetization and its relationship to the $\vec{H}$-field
I am particularly confused about the relationship between $\vec{M}$ and $\vec{H}$.
I know the simple matter relationship: $\vec{M}$ = $\chi_m \vec{H}$
Furthermore, we know that (referencing ...
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Magnetostatics: Compute internal magnetic field of a paramagnetic fluid
I have a question about calculating the internal magnetic field of a paramagnetic fluid. Assume that I apply an external magnetic field in the $x$ direction, equal to $H_{ext.,x}$ = 1 amp/m, on a ...
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Is the magnetic field outside a solenoid almost null for AC current?
Despite an answer to this thread, I'm not so sure the magnetic flux outside an infinite ideal solenoid is null whenever the current is AC. I've seen no real proof of that, and the Biot-Savart law ...
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Regarding the equation of continuity in magnetostatics
Griffiths says that for a steady current and uniform conductivity
DivE = (1/σ)divJ = 0. This is obtained by taking divergence of equation
E =(1/σ)J .
But from equation of continuity we know ...
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Where magnetism arises from?
Imagine we have a test charge and we push it, reaching a constant velocity of $u$.
Now the electrons inside of the cables reach a velocity of $v$. Our goal is to measure the electric field that the ...
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Necessary magnetostatics boundary conditions to yield a unique solution?
There are two magnetostatics boundary conditions for magnetic flux density and field intensity:
$$\bf n \times (\bf H_1 - \bf H_2) = 0 \tag1$$
$$\bf n \cdot (\bf B_1 - \bf B_2) = 0 \tag2$$
where $\...
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What are the necessary conditions for a current to be steady?
Does the divergence of the volume current density have to be zero for the current to be steady? If so, what are other other conditions? If not, what are the conditions for a steady current in general?
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On the definition of magnetic field intensity
In magnetostatics theory, the magnetic field of any magnetic body with magnetization $\mathbf M$ is equivalent to that of a volume current density $\mathbf J_{m,v}$ and a surface current density $\...
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Is there a specific boundary condition in magnetostatics on sharp edges?
The magnetostatics boundary conditions states that the parallel field intensity $\mathbf n \times \mathbf H$ and the normal flux density $\mathbf n \cdot \mathbf B$ must be continuous when crossing ...
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Can magnetic permeability be exactly equal to 1 in Gaussian system of units?
In the Gaussian system of units, $\mu >1$ for a paramagnetic substance, while for a diamagnetic substance $\mu<1$. For free space it exactly equal to unity. My question is: is there any ...
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Apparent contradiction in Ampere law for a solenoid
This picture in Wikipedia is supposed to explain the solenoid formula for the magnetic field $$B l= \mu_0 N I$$
(assuming steady currents).
But this would be true if one consider only the part of the ...
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On the singularity of Biot-Savart's law inside a current-carrying conductor
When using Biot-Savart's law to compute magnetic flux density on a field point away from a current source point, the integrand is finite; however when using it to compute the field inside the source ...
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Example of information travelling faster than the speed of light?
In the following situation, information seems to travel faster than the speed of light. Is there a mistake in my reasoning?
Suppose we have an electric circuit. For times $t<0$, there is no current ...
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Coulomb gauge does not fix $\vec A$ uniquely. Is the solution to $\nabla^2{\vec A} = -\mu_0{\vec J}$ given in Griffiths unique?
With the Coulomb gauge $\nabla\cdot{\vec A}=0$, and $\nabla\times\vec A=\vec B$, the vector potential satisfies the Poisson's equation, $$\nabla^2{\vec A} = -\mu_0{\vec J},$$ which for $\vec J\to0$ ...
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How to justify the direction of the magnetic field formally, in symmetrical situations?
I know the right hand rule and I know how to use it, what I am asking for is a formal argument for situations where symmetry is in our favour.
The right hand rule is a kind of mnemonic but it doesn't ...
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How porous can a ferromagnet before turning paramagnetic?
As there is an inherent size limit to magnetic domains, as the porosity of a ferromagnetic material increase, there will be a point in which a static magnetic field will not be possible.
There are a ...
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Can the electric field have closed field lines?
In electrostatics, we know that $\vec{\nabla}\times\vec{E} = 0$ and so, the field lines can't form loops. But when we have time-dependant magnetic fields, there's the Faraday-Lenz law which tells us ...
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EM Lorentz force field flux in the air gap of a parallel plates charging capacitor?
For a charging/discharging capacitor, simultaneously to the electric field created by the displacement current during charge/discharge cycle, a magnetic field is also generated in the area inside the ...
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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 gap of a two parallel plates capacitor?
We can magnetize an iron piece (i.e. permanently given enough field strength) by putting it inside a solenoid strong homogeneous field and charging/discharging the solenoid several times.
I am asking ...
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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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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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