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.
Questions tagged [magnetostatics]
358 questions
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Force Lines of Magnetic Field of Circle Loop
Magnetic field of a loop with a stationary current in a xy plane with center in the origin is usually computed on the z axis. Out of the z axis the calculation results into elliptic integrals. I would like to know whether some geometric analysis of…
Svata
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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 infinitely many surfaces that share the same…
Saksham
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Magnetic vector potential of a current loop results in 0 in all space
I tried applying the following relation
$$ \vec{A} = \frac{\mu_0}{4 \pi} \int_\Omega \frac{\vec{J}}{\vert \vec{r} - \vec{r}^\prime \vert} dV$$
To find the magnetic vector potential on all space of a current loop of radius R carrying a current I,…
JS Cruz
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Magnetic field and magnet
We know that magnetic does not do any physical work . Now consider; we attached a magnet in a wall with help of a tape. Now we bring a magnet near to other magnet and released we see that magnet will displace towards other magnet. How was the work…
Manoj Ghosh
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How do magnetic shields work?
I've come across the fact that magnetizable material can shield magnetic fields. For example, if I put a ferromagnetic plate between the magnet and a nail that is hanging on a thread pulled towards the magnet, the nail will eventually fall down when…
user424862
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Conditions on expressing magnetic field in terms of curl of current density
Given a current density distribution $\mathbf J(\mathbf x)$ inside a closed bounded region $\Omega$, the magnetic field at any point $\mathbf y$ outside of $\Omega$ can be expressed as
$$
\begin{aligned}\mathbf B(\mathbf…
Jasper
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Magnetic field outside a sphere containing surface charge rotating at a uniform angular velocity
Say I consider an amperian loop surrounding the sphere, wouldn't the net current through it be zero as the current entering the loop due to one half of the sphere and the current exiting in the opposite direction are equal in magnitude? However this…
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How does an external magnetic field affect the magnetization inside a permanent magnet?
I am looking for a first-order correction on the intensity of the field generated by a (neodymium) magnet in the presence of an external magnetic field $B$ (possibly generated by another magnet). For simplicity, we may assume that $B$ and the magnet…
Georges
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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:
$\vec{\nabla{}^2}\vec{A_r}=0$
$\vec{\nabla{}^2}\vec{A_\phi}=\frac{\mu}{\mu_0}\vec{J_\phi}$
$\vec{\nabla{}^2}\vec{A_z}=0$
in cylindrical coordinates where…
Sophia
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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 parallel to the wire from either end).
If we try to…
David
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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 div J = dρ/dt. For steady current, div j is 0…
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Curl of a Magnetic Field Produced by a Surface of Current
If the curl of the magnetic field, produced by a volume of current, $J$, should be given by $ \nabla \times B = \mu_0 J$, then should the curl of a such field, produced by a surface of current, $K$, be given by $ \nabla \times B = \mu_0 K$ (or…
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Magnetostriction: Equation and value of the relative length change
Magnetostriction is a property of materials that causes them to change their length along the applied magnetic field.
In the German Wikipedia an equation for the relative length change of materials is given.
$\lambda_\| = \frac{\Delta l}{l_0}$
Below…
HolgerFiedler
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Magnetic field on an arbitrary point ON a Current Loop
Consider this situation given above. We have an arbitrarily shaped theoretical current loop made up of wire of zero radius in free space. Away from all electromagnetic, gravitational interactions.
Meaning, THERE IS NO EXTERNAL FORCE ON THE CURRENT…
JjJot
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magnetic field doing work on a wire
I am a tutor and during a session today, a thought occurred to me. I've long been told (and been telling) that magnetic fields do no work, but it's pretty easy to imagine a situation in which a magnetic field DOES do work. If two wires have parallel…
MmmQuarks
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