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4

If you for example look at the Biot-Savart law, you'll see that the magnetic field decreases with the square of the distance when you move away from the current that generates the field. The same goes for a static magnet: you can in general expect that $\mathbf{B}(\mathbf{r}) \sim 1/\|\mathbf{r}\|^2$ in the magnetostatic case, which means that ...


3

The electric forces that we see in nature are due to separate charges (electric monopole charge), however, all matter ever isolated to date, including every atom on the periodic table and every particle in the standard model, has zero magnetic monopole charge. Therefore, the ordinary phenomena of magnetism and magnets have nothing to do with magnetic ...


3

Yes the energy $u$ stored in a field $B$ in a region with permiability $\mu$ is given by: $$u = \frac{1}{2}\frac{B^2}{\mu}$$ So if you double $B$ then $u$ gets quadrupled and if you increase $B$ by a factor of $10^{10}$ then $u$ increases by $10^{2\times 10} = 10^{20}$. I'm not quite sure about the assumptions that go into the above formula however (I'll ...


2

Remember, $\vec{\nabla} \times \vec{B} = \mu_0 \vec{J}$, and $\vec{J}$ will be zero anywhere except on the loop itself, where it will be singular. Do you mean, perhaps, that the line integral around the loop equals the current, a la Ampere's law?


2

Expanding on Jan Dvorak's comment: When you change the magnetic field inside a loop, an emf (electromotive force) will be generated. Now if you have two loops, each of these will experience the same e.m.f. When you put them in series, you have a coil with two loops, or two coils with one loop. No matter which way you look at it the voltage across them ...


2

There's an electric component to the Lorentz force: $$\vec F = q(\vec E + \vec v\times\vec B)$$ In the frame of the particle where its velocity is zero, the force acting on the stationary particle would be interpreted as being electric, since the magnetic field $\vec {B'}$ only acts on moving charge, and is given by: $$\vec {F'}= q'\vec {E'}$$ In your ...


2

No, the signal will not (usually) be corrupted by outside electromagnetic radiation. Classical electromagnetism tells us that electromagnetic waves interact linearly. Therefore, when microwaves emitted from a nearby tower pass through the fiber, they will interfere with the signal locally, but as the waves pass through each other, they will come out on the ...


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Theoretically, yes: the kinetic energy of the metal is due to the work of the electrical source that maintains the current. This is what happens: in order for the metal to feel a magnetic force, it needs to have some magnetic moment (which can change over time). When this magnetic moment moves, it creates an induced e.m.f. on the wire that carries the ...


2

The shape is caused by normal-field instability. This is the condition where these small 10nm droplets of ferrofluids are described by Maxwells equations where the divergence of the B field is zero and the curl of H is zero. The imposed magnetic field leads to a stress condition mismatch at the interface between the internal of the droplet and the outside. ...


2

I already got the answer. because transformers simply doesn't work in high voltage environments. High voltage environments causes dielectric breakdown which reduce the transformers function which is bad. Tesla coils fix this problem.


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A magnetic fiels behaves pretty much as an electric field. Actually you can transform one into another just by changing your inertial frame of reference to a moving one. The imposrant different for this example is that isolated magnetic charges (magnetic monopoles), do no seem to exist, so the magnetic field of a magnet will take a similar shape than that of ...


1

Magnetic hysteresis is inherently irreversible in the sense that no matter how slowly one executes a time periodic current drive and hence an $H$ field around a ferromagnetic sample the resulting $B(H)$ curve encloses a non-zero area representing the dissipated magnetic work. This is an interesting example of a thermodynamic system where a quasi-static ...


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Your instincts are spot on. While it’s still common for people to refer to electricity and magnetism as different phenomena, they’ve been formally unified since Maxwell’s 1873 paper on the subject, and they were known to be intimately related for decades before that through Faraday’s work among others. “Electromagnetism” covers all of the behavior of ...


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What I assume the book is trying to say is that, as the electrons move downward (because they are part of a current), the magnetic field bends their path toward the left. This is the horizontal motion that the book mentioned. But of course the electrons can't run off the edge of the bar, so they pile up at the left side, leaving unmatched positive charges ...


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In my experience (with ferroxcube materials) nothing happens. In fact, to change the magnetic properties the magnetic domains inside must be reoriented. But the force excerted by the second magnet is not strong enough to do so. But one can magnetize a non-magnetic piece of iron (for instance the tip of a screwdriver) by moving it over a magnet.


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It is the electric field that does the work, not the magnetic field! When one has current in the loop, it can undergo a voltage drop or rise according to the inductance of the coil. Inductance relates to the electric field and its work. See: http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction "The induced electromotive force in any closed circuit ...



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