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Many astrophysical plasmas are well modeled as perfect conductors. Ideal MHD assumes this limit. As a result, there is no electric field in the fluid's rest frame. In other frames, we generally have $\vec{E} = -\vec{v} \times \vec{B}$, so there is an electric field. However, the perfect conductivity constraint means we don't have to model the electric field ...


8

The lack of the electric field in modeling plasmas stems from the Lorentz force, $$ \mathbf F=q\mathbf E+q\boldsymbol\beta\times\mathbf B $$ where $\boldsymbol\beta=\mathbf v/c$. For most astrophysical plasmas, the force is zero, so we have that $$ \mathbf E=-\boldsymbol\beta\times\mathbf B $$ So any time we see an electric field, we can simply replace it ...


3

There aren't E and B fields in the entire universe. For example, there are no electric fields inside a conductor. I'm sure there are quite a few other such examples. If you mean "why are there electromagnetic waves throughout the entire universe?", one answer is because the radiation field drops like $1/r$, so the field from a single source never ...


3

You're almost there. For the symmetry argument: first notice that Faraday's law, $\oint\textbf{E} \cdot d\textbf{l}=-\frac{d\Phi}{dt}$, looks the same as Ampère's law from electrostatics: $\oint\textbf{B}\cdot d\textbf{l}=\mu_0 I$. Now consider a current (or a homogeneous current density) pointing in the positive $x_3$-direction. What is the direction of ...


3

The Biot Savart law is $${\bf B} = \frac{\mu_0}{4\pi} \oint \frac{ I\, d{\bf l} \times {\bf r}}{|{\bf r}|^3}$$ In this case $d{\bf l} \times {\bf r} = dl\,|r|$ directed along the loop axis and integrating around the closed loop leads to a B-field magnitude $ B = \mu_0\, I/2R$ as you suggest. However, I think there is a problem with your application of ...


3

Radio waves are not perturbed by external magnetic fields. If you put your radio receiver in a magnetic field you may experience some electrical noise which blinds the signal, but this is still there untouched and your neighbour downstream would confirm this. Even if the generic wire is a correctly matched antenna, the power that is absorbed from the wave ...


3

This is how I like to visualise it. If you imagine you have a core like in my first image then the flux lines are like what you would expect. Now remove the right half of the core and your're left with your transformer image. There is still magnetic flux in the air, but it is left out normally as it is negligible in comparison with the flux in the core. ...


2

Yes, the Earth's magnetic field does rotate with the Earth. There is a simple way and a complicated way to explain this. Firstly the simple way: the magnetic north pole and the North Pole are not at the same point. That means if the magnetic field did not rotate with the Earth the magnetic north pole would rotate once around the North pole every 24 hours. ...


2

The answer is positive. This is due to the fact that the equations describing how currents generate the field are linear. The solution is obtained by a suitable inverse of the linear operator associating currents to fields. It is fundamental to observe that this inverse operator is linear because the boundary conditions satisfy the superposition principle ...


2

As far as I know magnetic field can be changed by another field. Usually this takes alot of time. Magnetic field would not be changed after it stops interacting with another field. Magnetic field can affect the orientation of domains, and not the spin of electrons. Pardon me if I am wrong.


1

Reluctance = $\dfrac{l_e}{\mu A_e}$ where..... mu is the absolute permeability of the material, $\mu_0 \mu_r $ $l_e$ is the circumference of a circle at a radius r and $A_e$ is a small cross sectional area. The circle I refer to only relates to the cross section of the torus and r is the radius from the centre (where the wire is). All these reluctances ...


1

This is really just an extension of Jaskaran's answer, but the answer to your question is yes and here are some examples: if you stroke an unmagnetised piece of metal with a magnet then you can magnetise it (as demonstrated in elementary physics classes across the world!) if you expose magnetised metal to an oscillating magnetic field you can demagnetise ...


1

Probably because matter on a large scale is electrically neutral and therefore the electric effects cancel out .This asymmetry arises from the fact that atom as a whole is electrically neutral.


1

Equations for magnetic interactions between objects tend to be a lot more complicated than for electrostatic forces. This is because while electric fields are produced by and exert forces on charge, a scalar, magnetic fields interact with electric currents, the flow of charge in a particular direction, which is a vector quantity. This makes the equations for ...


1

A paramagnetic material is something that has a magnetic field even without the presence of an external field, but the external net effect is roughly zero. The internal atoms or molecules of the substance have magnetic diopoles meaning the substance itself is made up of billions of tiny magnets. The thing with paramagnetic materials is these dipoles are ...


1

Your calculation of $B$ using Ampere's Law is not correct. The integration surface should have its area perpendicular to the current and should have one of the sides go parallel to $\vec{B}$. The choice of surface, when using that form of Ampere's Law, is usually a square or rectangle. That's why using it for a single loop does not work, because $\vec{B}$ is ...


1

You probably misapplied Ampere's law. This law is usually used to find magnetic field only in special cases when the contour integral can be found as a function of single field value based on symmetry. Magnetic field of a circular current loop is not so simple and Ampere's law cannot be easily used to find it. In such cases, the method of choice is to use ...



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