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Jul
27
comment How was Newton able to guess that gravitational force is inversely proportional to distance squared?
@BrandonEnright which basic assumptions are you talking about?
Jul
22
comment Is a falling, perfect sheet of fluid possible to create?
@M.Herzkamp, I've only seen/heard of liquids in a vacuum on this: youtube.com/watch?v=8F4i9M3y0ew
Jul
18
comment How to solve the Laplace Equation in the hollow square region?
There are a lot of examples in, for example, Griffiths intro to electrodynamics ch. 3, where there's a discontinuity in the potential at the corners but a convergent solution exists.
Jul
18
comment Do Electromagnetic Waves really propagate through continuous Induction?
I think this is false, in the concrete sense that if you put a stationary electron in the path of an EM-wave, it would accelerate.
Jul
15
comment Can we measure rates in real time?
@BrysonS. But the two measurements can guarantee an exact velocity at some point in time within an interval. That's pretty good, and is contrary to the second sentence of your third paragraph.
Jul
15
comment Can we measure rates in real time?
Can I state the obvious? Every measurement must occur over a period of time. So we could never measure velocity at an exact point in time any more than we could measure position at an exact point in time. But you can get an instantaneous velocity by measuring it at two points in time! Apply the mean value theorem and say, "at some time between t=0.000 and t=0.001, the car was moving at exactly 20 meters per second".
Jul
14
comment Divergence of a field and its interpretation
Let us continue this discussion in chat.
Jul
14
comment Divergence of a field and its interpretation
@Subhra The energy density of the electric field is $\frac{1}{2}\varepsilon E\cdot E$. The energy density of the magnetic field is $\frac{1}{2\mu}B\cdot B$. With zero current density, they are related by $\nabla \times B=\mu \varepsilon \frac{\partial E}{\partial t}$ through the maxwell-ampere equation (assuming J=0). Differentiating the first eq over time gives $\varepsilon E\cdot \frac{\partial E}{\partial t}$. Substituting the third equation gives that the rate of change of energy density of $E$ is $\frac{1}{\mu} E\cdot (\nabla \times B)$. This is being done by the magnetic field.
Jul
14
comment Divergence of a field and its interpretation
@Subhra and the magnetic field does have a source of energy. In the same way that a block resting on a table has a "source of energy" - someone lifted it up there in the first place. Some current density or changing electric field lifted the magnetic field up, and to do that it took energy. This is an important principle of the inductor.
Jul
14
comment Divergence of a field and its interpretation
@Subhra There are further ambiguities in what you're writing. For example, a constant magnetic field does no work on a moving charge, that much is true. But "B does no work" is less true. Through Ampere/Maxwells's equation linked, $\nabla \times B$ is proportional to $dE/dt$ (when there is zero current density). Since $E$ stores energy, $B$ must be doing work! It isn't doing work on a charged particle, however. It is doing work on a field.
Jul
14
comment Divergence of a field and its interpretation
@Subhra You are using terminology too informally. This, I think, is masking some deeper misunderstanding. How can you say "B does no work" and then start a sentence with "work done by B"?! I know what you mean, "a direction changing force caused by B", but still. You should also stop using the word "source" if you don't mean it! If you ask someone to name a source of a magnetic field, they might answer a wire with a current going down it. In some sense, the wire is a source of the magnetic field. We still have $\nabla \cdot B=0$, I just mean to demonstrate that "source" is ambiguous.
Jul
1
comment can we calculate velocity of a spinning apparatus by just analysing the frequency of sound emitted by it
I'd have to experiment but I think the whole thing could be much more complicated. You also have to worry about what modes you're exciting on the motor casing! (though of course the driving one would dominate) Come to think of it, I'd love to see an animation of the frequency spectrum of an electric motor over various frequencies.
Jul
1
comment can we calculate velocity of a spinning apparatus by just analysing the frequency of sound emitted by it
@DanielMaksuta I think you misread the question. The question is not like an emitter of sound attached to a carousel, but like a motor in a black box turning an axle.
Jun
30
comment How can Lorentz contraction be “directly” measured?
@Ruslan Note that "Rotation" shouldn't be taken on face value. Take for example this: en.wikipedia.org/wiki/… In diagram 2 a dimple actually forms in the sphere! (Hint: you're actually looking at the projection on the spatial axes of the intersection of a tilted cylinder with a cone).
May
18
comment Everything is a Photon
@JoshuaMeyers en.wikipedia.org/wiki/Matter_wave gives that $p=\hbar k$ and $E=\hbar \omega$ still hold, but instead of $E=p^2/(2m)$, we have $E=p c^2/v$. So $\hbar\omega=\hbar k c^2/v$. $E^2-(pc)^2=(mc^2)^2$ then simplifies to $(\hbar k)^2=(\gamma m c^2)^2=p^2$. So we just get $(\hbar k)^2=p^2$ again.
May
18
comment Jackson, Classical Electrodynamics - page 97: how to deal with the indexes of a series to obtain Legendre polynomials
Can you edit out the note that equation 1 is not written down correctly now that it's been fixed? Thanks.
May
11
comment Are intergalactic voids inertial frames?
@rijulgupta the principle of equivalence says that being in a frame where objects experience a gravitational force is equivalent to being in a nonintertial frame.
May
3
comment How does light bend around my finger tip?
@Virtlink, the ray model is useful and intuitive, just like incorrect ideas can be useful and intuitive, but light is not a particle travelling through space, it is a wave travelling through space (under the classical E&M picture).
Apr
28
comment How can I compute the angular velocity of a triangle formed by three particles knowing their instantaneous positions and velocities?
I don't understand. Why are we interested in the angular velocity of $\hat{n}$? If it is spinning perpendicular to its plane, won't $\hat{n}$ be zero, while there is nonzero angular velocity?
Apr
25
comment Does electricity flow on the surface of a wire or in the interior?
Great example of litz wire!