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After the switch is shunted from the battery to a short there is emf developed by L di/dt across the inductor. However, there is also voltage, established as an electrostatic E field equal in magnitude but opposite in polarity to the electromagnetically generated E field, both fields resident...

If an inductor (e.g. solenoid) sees a time-varying externally generated B field within it it will generate an emf . Think an open secondary winding of a 2-coil transformer. There is an E field in each winding such that per winding ## emf = - d\phi/dt = \oint \bf E \cdot \bf dl ## around the...

I wanted the time to reach equilibrium, not just the final values. Knowns: effluent rate dV2/dt loop gain component ## k_1 ## influent purity ## \rho_1 ## Reference volume ## V_r ## The fly in the ointment is admittedly the evap rate which I have to estimate. I do have empirical data of...

My question was 'what is ## \rho(t) ##.' The link I don't think applies to my situation: "The equation can only be applied when the purged volume of vapor or gas is replaced with "clean" air or gas." In my case the impure solvent (water) is replaced by less impure solvent. (Of course I could...

This cooler would not work - for long. There is no provision for effluent so reservoir salinity would build up until the pads are solid salt! (Inlet water, depending on your area, always contains impurities, particujlarly salts).

I should add that deriving ## \rho_{~final} ## does not require solving for the time function but I also wanted an idea of the time required to reach (close to) equilibrium. Besides, it looked like a good physics challenge.

Well I tried ... o:)

Nope, just give me ## \rho(t) ##. cf. post 6 and scrutinize the jpeg.

cf. post 6.

I am looking for the expression for ## \rho(t) ## so I can optimally adjust the effluent flow rate. Basic swamp cooler operation: Water runs over pads; evaporates; that cools the pads, then air is blown past the pads into the house. If the air is very dry a swamp cooler can produce air almost...

Guys, this is a real-life problem, especially now in Phoenix in June! Wolfram Alpha gave me this: Must be easier than that??

Inductance would probably increase, not because it's a magnet but because it's probably a high-permeability material like iron.

Well that is just fine!

My book says that means that there is no current through it. I do not understand why there is no current through it if the magnetic force is perpendicular to it? Your book does not say that. It says no current is induced in the horizontal sections but there is current induced in the vertical...

Just intuitively, disregarding the formula altogether - one would expect the frequency to increase as the water level rises. That's because the dry-glass part gets shorter. Typically if a taut string or whatever is shortened the frequency increases (Mersenne's law: one would think that...

Wave functions with differing coefficients, real or complex of any magnitude, represent the same wave function. Normalization is required if observational probabilities are desired. Normalization makes them equal.

If ## \bf A = rz~ \hat {\bf \theta} ## then ## \nabla \times \bf A = (z/r)~ \hat {\bf k} - \hat {\bf r} ## and not what is given. Different fields ??

Or if you just pick a cable with ## Z_0 ## matching the transducer, then the receiver can be any impedance ## Z_L ## , again with no attenuation or distortion, but with gain = ## Z_L/(Z_L+Z_0) ##.

If he can make his transducer, cable chas. and load impedances roughly the same there is low or negligible capacitive load effect regardless of cable length; he just gets a gain of ~1/2 with pure delay. Ideal cable assumed of course).

Your E field is uniformly in the direction you show. Don't be confused by other E field orientations. As post 11 says you need to take the dot product of the E field, and the local normal, at each point on each surface. On the top & bottom ones the E field and normal are aligned but on the...

If you move a dielectric into a vacuum with the battery connected that statement is incorrect. Yes the charge density on the plates increases but the E field stays the same. Again, assuming the gap is fully filled by the dielectric. But maybe that is not what you meant to say?

That's if there is no battery connected. You specified a battery connected. Horse of different color. As long as a battery is connected the E field is the same whether your airgap is filled with air or with a dielectric.

Why do you add E_0 + E_i ? There is only one electric field as I said. It's V/d. I see no meaning to your ## V_i ##. There is only one voltage and that is the voltage between the plates, again irrespective of presence or absence of dielectric.

But: there is only one E field and that is E = V/d. V is the battery emf. It makes no difference if there is a dielectric present or not, assuming the dielectric fully fills the interplate space. EDIT: If you remove the dielectric, ## Q_{free} ## changes but E does not. ## Q_{free} ## is the...

For me to help you need to define your terms.

You will notice that there is a problem as ## r \rightarrow 0 ##. So you need to take the finite radius of your wires into account. If you do that the average is ## B_{avg} = ~(2\int_a^{d-a} \mu_0 I/2\pi r~ dr)/(d-2a) ## where ## a ## is the wire radius. Not sure why you want this but there...

You hold a short, thin rt. circular cylinder , length l, made of hi-mu metal, e.g. iron, coaxially and near a solenoid (not inside). The axial B field will be stronger near the solenoid & weaker as you move away axially. There will be a force applied to the near end surface of the cylinder...

@ofirg55: Not sure what you mean by "T". I assume "phi" is the more usual "psi". So let me paraphrase what I think you're saying: Given a (1-dimensional) wave function ## \psi (x) ## we state that the probability of a measured particle's position is ## \psi (x) \cdot \psi^* (x) ##...

In post 11 bottom right picture that looks wrong, if the intent is to demonstrate dispersion. Different color rays will not focus on the same spot. E.g. if the screen image distance is adjusted so as to render an exact focus for green light, then a red beam would focus behind the screen...

Quoting the OP: "That applied force increases the momentum that is carried in the currents induced by the magnet." Clearly he was referring to the momentum carried by the electrons, not the magnet. It's a subject for quantum physics.

I think we're in the realm of quantum physics when we deal with electron momentum.

I deleted my posts (##25 ff.) since my argument was not really relevant. @ergospherical 's explanation is certainly correct but his statement "The assumption of a constant and uniform magnetic field means there is a well defined electric potential field" is IMO not obvious to an introductory...

Yes, just as Mr. Faraday said: ## \oint \bf E \cdot \bf {ds} = emf = -d\phi/dt ## !

Think two batteries of identical emf connected + to + and - to -. Is there an emf between the + and the - contacts? Is there current?

Post 12 makes an impiortant point: the superposition of rolling and translational motion, one of which generates zero emf, enabling significant solution of the problem. To answer the question of how there can be an emf without current: what about the right half of the ring? Doen't it generate...

https://tutorial.math.lamar.edu/classes/de/laplaceseqn.aspx Bit of a challenge as you can see.

You need to read Ampere's law carefully.

You will not get much in the way of quantitative results. Trying to analyze one coil turn at a time is hopeless. Just calculating the flux in a 1-turn coil with given current is beyond any introductory physics course. You'd have better luck with a long solenoid in which case the two...

Here's another proof: Say you have 4 unit-area plates stacked close together vertically. 4 plates, numbered 1 to 4, left to right. 3 gaps. Number the surfaces 1 thru 8 left to right. Put charge Q on plate 1 and -Q on plate 4. Assume the center two plates have zero charge. Fact: the...

I think the B field remains the same so of course the H field is reduced by ## \mu_r ##. But, as I said, I'm not sure.

My original idea was that the B field was not augmented at all since then I thought ## \nabla \cdot \bf B = 0 ## would be violated at the boundary between air and the core. I thought all the core did was increase the inductance. But then I never figured out why that was a good idea either -...

I'm aware of the alleged magnetic field "concentration" effect by the ferrite core, but do you know of any analyses of the quantitative effect? By how much is the B field amplified? By the relative permeability? I have been unable to find a good analysis of this effect.

Yes. The nice thing about running a loop antenna of typical size (say 1"=10" diameter) at 1 MHz is that the B field is essentially uniform across its area. So you can apply Faraday's law to determine the emf as ## -d\phi/dt # times the number of loops.

Analogies may be well and good for the layman but not if you want to understand physics which is all based on experiments - irrefutable experiments.

No, because there is no B field induced inside the tube. Also, even if there were, it would not generate an axial force.

Using only Snell's law and small-angle approx. I can corroborate the answer. Do we agree it's a virtual image?

Check. Thanks.

I think the problem statement needs clarification: - object is in water or in air? - object is 10 cm to the left or the right edge of the plate?

So do you have the book? If not, where did the pics come from?