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5

Conclusion: The particles are, in-fact, magnetic This is doubtful. There are two possibilities here: If the objects used to grind (let's call them grinders) the dust grains were made of a ferromagnetic material like iron/steel and/or nickel, then it is possible that the grinders deposited some material onto the dust. There is no reason to think that ...


5

We usually do not talk about a "color electric field" to begin with. The strong force is treated fully relativistically from its beginning. If you want, you can define a "color electric field" and "color magnetic field" from the strong field strength tensor $G_{\mu\nu}^a$ in exact analogy to electromagnetism as $E^a_i := G_{0 i}^a$ and $B^a_i := \epsilon_{...


4

$\mathbf{S}$ is the spin operator. It is a vector operator that acts on spinors. It will have three components $(S_x, S_y, S_z)$ and for example if you take the $z$ axis as your spin measurement axis, you define spin up and down as the two eigenstates of $S_z$. It can be shown that in matrix form $S_i$ is proportional to the Pauli matrix $\sigma_i$. ...


4

I assume the magnetic property you're thinking of is ferromagnetism. If so then no, a gas of cobalt atoms would not be ferromagnetic. If you take a single cobalt atom you'll find it has a magnetic moment i.e. it behaves like a tiny magnet. This is because the cobalt atom contains unpaired electrons, and there are lots of atoms like this. However if you take ...


4

Considering only the spin, ignoring translational DOF, the Hamiltonian is $$H = -\mu ~\mathbf{B} \cdot \mathbf{S}$$ If $\mathbf{B}$ is directed along $z$, it's easy to see that $S_z$ states are energy eigentstates and thus are stationary. Applying time evolution and taking the expectation value shows that if the spin is not oriented along $z$ initially, ...


3

The mechanisms of pole reversal are not fully understood, but current theory is supported well by mathematical simulations. The primary structure understood to be responsible for advection, the generation of the Earth's magnetic field, is the outer core, a fluid layer comprised primarily of iron and nickel which lies between (roughly) 2900 to 5200 ...


3

For an applied AC voltage, the primary coil has an impedance from self-inductance which limits the current (amperes) flowing through the copper (unless you draw current from the secondary coil). For an applied DC voltage, the impedance from self-inductance is zero, which causes a large current to flow. This current heats up the wire with a power $P=I^2R$, ...


3

You need to look up the Helmholtz Theorem and similar results that will basically give you ACuriousMind's Answer. But a way I like to visualize this is through the Fourier transform; in Fourier space the curl $X\mapsto\nabla\times X$ and divergence $X\mapsto \nabla\cdot X$ become simply the cross $\tilde{X}\mapsto k\times\tilde{X}$ and scalar$\tilde{X}\...


2

Interesting. I assume they are using a blank of NdFe magnetic material and then using a small area coil which is then pulsed to create a programming field. Same way as a conventional magnet is magnetized. However, their coil will have a much smaller diameter and can be moved across the magnet blank in X-Y steps to create multiple magnetic domains within the ...


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That's the Gertsenshtein effect. It is the theory that light passing through a strong magnetic field will produce a gravitational wave.


2

Direction of deflection of electrons in magnetic field It is not the full picture you are describing. A moving electron in a magnetic field gets deflected according the rule $ \vec F = q \vec v \times \vec B $. This vector product has a direction and and this is what we observe in natur: all electrons get deflected in the same direction. Otherwise no ...


1

you are basically trying to undergo a transition from a law which is valid for static charges(or non relativistic speeds) to one which is valid for steady currents. That is why, simple differentiation is erroneous and does not include any magnetic field term in dE/dt.


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The state is still $ \psi (t=T) $ right after the rapid change of B field to y-direction because the system doesn't have enough time to response the change.


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An isolated charge (like, an electron) is produced by ionizing an atom, using energy to pull a single electron free of the atom and pulling that charge far from the opposite-charge ion. So, it DOES take energy to isolate the charge. The isolated charge has an E field around it, but the original uncharged atom had none. Similarly, when you apply a ...


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I'll answer more in a clinical perspective. I don't know about extreme situations when the spins of your organism's atoms are rearranged in a lethal way, but as far as MRI magnets go, the first concern when using MRI equipment is the possible induction of electric currents inside the human body. These concerns are more prevalent for investigation MRI ...


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A 2013 paper by Shtanov and Sahni (already mentioned by Ben Crowell in the comments) says that the modes grow exponentially in conformal coordinates, and Barrow et al overlooked the fact that the conformal time changes very little during and after inflation. A 2014 preprint by Tsagas, one of the authors of the original paper, cites Shtanov and Sahni and ...



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