3
Mathematically you can surely see that $\vec{J}=0$ outside the wire and therefore the differential form of Ampere's law demands that $\nabla \times \vec{B} = 0$.
I guess what is confusing is that curl is often described in terms of "curling field lines", but that isn't entirely accurate - straight field lines can have a curl and curved field lines ...
3
There is an electrical component called a Möbius resistor that takes advantage of this weird geometry.
The current flows in through the wire marked (+) and out through the wire marked (-). Because current flows in both directions around the ring, only a negligible magnetic field is generated. This can be important in high-power, high-frequency electrical ...
3
Since all calculations did by hft actually is right, we only proposed picture for this question how coil looks like from three different point.
2
You don't need to think of the whole loop all at once. Each of the four legs of the "loop" can be considered one at a time.
Also, the problem is in a sense two-dimensional, since the way it is specified the loop is fixed such that only torque about the x-axis matters. So if it is easier, you can just draw two-dimensional diagrams only showing y and ...
2
The magnetization in the iron starts precessing immediately at an angular frequency given by $\gamma H$. The gyromagnetic ratio, $\gamma$, has a value of about 28 GHz per Tesla. Eventually the oscillation dies out due to various damping phenomena in the material and the magnetization tends to align with the field. In most cases this takes just a few cycles. ...
1
The inductance of the coil resists sudden changes in the current flow. At the instant you close the switch, the current-versus-time curve has a very sharp kink in it right at its origin (at time = zero) indicating a very very sudden, discontinuous change in the current, and the inductor fights back against that change.
This is entirely analogous to the ...
1
Here is a diagram of a vector field like the one you're talking about:
If you insert a paddle wheel ("curl meter") in this field, then the stronger field on the left compared to the right would tend to produce a clockwise torque, but the angles of the top and bottom would tend to produce a counterclockwise torque. In the actual field, the radial ...
1
For a 'uniformly' magnetized material, the longitudinal (down the length) component can be continuous around the loop, but both the transverse (across the width) and perpendicular (through the thickness) components must encounter a 180-degree change somewhere around the loop.
If the magnetic anisotropy is high, the magnetization may make just a single ...
1
The answer is easily obtained by remembering what creates the permanent magnetic field. All subatomic particles are magnetic dipoles and in some materials - natural or man-made - subatomic particles are aligned by their magnetic dipoles in such a way that a stable macroscopic magnetic field is present.
The stability of permanent magnets is a relative thing. ...
1
There is no simple, exact formula for this. What you are looking at in the first two links are a couple of approximations. For a comprehensive treatment of this subject, see this document by David Knight.
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The direction of the magnetic field generated by a loop in which current is flowing is given by the right hand rule
Therefore the magnetic field through the second loop will be
If the current inside the first loop increases so does the magnetic field it generates, and so does the magnetic flux through the second loop. By induction this changing magnetic ...
1
Field lines forming closed loops does not mean the curl is non-zero at all points in space. Curl is a local property defined through derivatives, so the curl at a point just depends on the field around that point. The curl operation doesn't depend on what the field is doing elsewhere.
In this example the current density $\mathbf J$ is $0$ outside of the wire,...
1
If the coil causes the angular momentum of the disk to change, then there is an equal and opposite change in angular momentum on the coil (assuming no outside forces or torques apply). If the coil is rigidly mounted, then there is a torque on whatever it's mounted to.
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Yes, the formula $E=\frac{1}{2}\epsilon_0 E^2$ is valid for electric field energy density in vacuum (or other medium such as air that interacts only very weakly with electric field) whether the electric field is purely electrostatic or general (including induced electric field or field of EM waves), but it is necessary that point charges or line charges are ...
1
Coil is not "inducing voltage", rather there is induced EMF being generated. Mobile charge carriers in the coil produce induced electric field, whose net total effect is quantified by so-called EMF (electromotive force).
Magnitude of this EMF is, due to Faraday's law, given by
$$
EMF = -L\frac{dI}{dt}
$$
The important thing is how quickly current ...
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