January 11

Polarisation and magnetisation

In electromagnetism, there is an field and a field. When there are objects present (as opposed to only vacuum), we often introduce the and fields, as tools to aid in our calculations. Still I would say and are the physical fields – the ones charged particles actually respond to.

When an object is penetrated by an electric field, its material can get polarised, which means that inside it, an electric dipole moment density arises. This is due to the so called "bound" charge density into which the positive and negative charges of the material arrange themselves in response to the felt electric field. The amount of polarisation is typically proportional to this field: . The bound charge contributes just like other, "free" charge to the electric field: . Note that this means that the polarisation in a point inside the object depends not only on the external, free charge, but also on the polarisation everywhere else throughout the object. Now, the field is defined as so that . Thus, is what would have been (save for a constant factor) if there were no ρ _b , i.e., if there were no object present.

Analogously to polarisation, we get magnetisation , corresponding to a "bound" current density, when a material is penetrated by a magnetic field. We define , which is what would have been (save for a constant factor) in the absence of the object. Finally, and here comes my question, I would expect to depend on the actual , but rather, one writes , as if the magnetisation isn't affected by what happens in other parts of the object. How can this be?

I just now realise that by rearranging, I can get , so now it looks like does feel (and in my mind therefore can be affected by conditions in other parts of the object). On the other hand, I can also get , losing the nice behaviour of the polarisation. How should all this be interpreted really? —Bromskloss (talk) 01:59, 11 January 2009 (UTC)

1. Only in a steady state with a universal dielectric (or magnetic medium) can D and H be described as (proportional to) "what would be there in vacuum". At interfaces, and , which breaks the analogy with E and B ; if anything is changing over time, terms like the displacement current also break the analogy.
2. Any arrangement of free charges and currents, dielectrics, and magnetic materials creates some set of fields, and the constituitve relations like only hold for that "final" arrangement of fields (as opposed to "what would be there"). Therefore it is incorrect to say that an equation like is somehow "missing out on B "; the H that appears is not independent of B but rather an alternative description of the same underlying pattern.

I got a question if water can explode?

Sometimes Im haulin a freight of it and its got hydrogen in it. Just like the Hindenberg,- and that exploded. What if the hydrogen escapes? I got lots of guys sodering around here and dont want no ambulance or clean up bill.--Troy da truck driver (talk) 02:59, 11 January 2009 (UTC)

Hell, you got to have one of those expensive degrees/toilet paper that I aint got to cut thru that thick fog of nebuloformulas. Please explain the article to me in beer drinking, wife beater English, if you'd be so kind.--Troy da truck driver (talk) 03:30, 11 January 2009 (UTC)

Audio quality - sampling rate versus bits per sample.

I'm trying to make a Arduino computer board play music and simple sound effects - such as you might find in a computer game. Various trade-offs in the $4 computer hardware(!) mean that I have a choice between higher frequency sampling rates and higher number of bits per sample. The system can't do both high sample rates AND high sample precision. If I want to double the sampling rate - I have to knock off one bit from the sample precision. If I want to add a bit of sample precision, I have to halve the sampling rate.

I can have 8kHz sampling rate with 10 bits of precision - or 16kHz with 9 bits or 32kHz with 8...and so on.

How do I make the trade-off to get the best quality of sound to the human ear? Does it make a difference whether I want to play sound, voice or sound effects? I also have an RC audio filter on the output - and I can choose the resistance and capacitance to do whatever filtering is needed.

SteveBaker (talk) 07:05, 11 January 2009 (UTC)

Steve, Would your system allow for "subband processing" with variable bit-allocation ? Say, using 12 bits/sample for 0-500Hz range (sampled at 1000 samples/s), 11 bits for 500-2000Hz and so on. The system design problem will be significantly more complicated but it will permit a better quality/processing-power tradeoff - at least if you were designing a system from scratch. Abecedare (talk) 21:47, 11 January 2009 (UTC)

Getting Younger Every Day

A 50-year-old Arctic explorer is 10 feet from the North Pole. He walks around the Pole, moving from West to East. As he does that, he crosses the International Date Line and the date moves back one day. He walks around the Pole again, and the date moves back again. How many times does he have to walk around the Pole to beome 25 years old? – GlowWorm —Preceding unsigned comment added by 174.130.253.174 (talk) 09:59, 11 January 2009 (UTC)

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