studiot

You are welcome. It is always a pleasure to discuss with someone who has a genuine interest. Ask away if you want more detail. I'm sure there are things you know from your experience that you might tell me one day.

What do you mean by stable? If you think about it something akin to the law of natural selection must be in operation. If a substance reaches an unstable state A then , by definition, it will not last very long in that state compared with a more stable state B. We do also distinguish two drivers in processes chemical and other interactions. Firstly a system tends to a state of minimum energy. Secondly a system tends to a state of maximum entropy. Changes occur that promote these tendencies, which may be in the same direction, but sometimes they are in opposition, and yet other times only one will be operating.

Here is something more interesting than just criticising. The formula n2 + n + 41 where n is 0,1,2,3, 4 .......... produces all prime numbers as far as n=39 and more prime numbers than any other quadratic formula as we run through the counting numbers. This was due to Euler.

Really? Perhaps you should think again. Whilst it is true that when you multiply two things together sometimes the result is the same as one of the two things so for instance The amount of juice squeezed is the number of oranges times the juice per orange So both the result and one of the multiplicands are juice This does not apply to force times distance, neither of which are energy. In fact your arithmetical manipulations mix up several different types of somethings (vectors, scalars and constants) in an original but inadmissible way.

Not sure what you mean by 'initial permeability@ but here is a learned article comparing mumetal superalloy and aluminium down to 10Hz. http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1139&context=theses Your proposed combined signal will be differentiated (filtered) by passage through/reflection from the shield. The calculations in the linked article will help estimate the extent of this filtering.

Electromagnetic radiation (EM radiation) has many properties. Frequency is relevant to the 'spectrum' which is a list of the whole range of frequencies of EM radiation we distinguish We give different names to different parts (ie different frequency ranges) of this spectrum, usually connected with their origin, So radio waves, radar, infra red, light waves, ultraviolet X rays and so on. There is some overlap of the frequency ranges so X rays (artificial) and gamma rays (natural) cover pretty much the same range of the spectrum. Note some are called rays because they tend to be 'line of sight' or directional at the scale of our planet Earth. This brings us to another important property - wavelength. The product of wavelength (l) and frequency (f) is the same constant © for all EM radiation so the higher the frequency the shorter the wavelength and vice versa. lf = c Old fashioned radio has a wavelength of many metres. How did your fox hole radio work out in the end? http://www.scienceforums.net/topic/94520-fox-hole-radio-help/#entry916439 Frequency also determines the energy of the EM radiation via the equation Energy = hf, where h is known as Planck's constant. Nasa has lots of good pics about more this and more properties. http://science.hq.nasa.gov/kids/imagers/ems/index.html

Do you know what a mathematical field is? The integers, both positive and negative, let alone the counting numbers do not satisfy the Field axiom for inverses for multiplication. http://mathworld.wolfram.com/FieldAxioms.html

So what patterns do you get if you put different shaped blocks of metal under the wood?

What's a naturalistic random process? Perhaps it is an example of this http://www.scienceforums.net/topic/102080-language-use-by-specialists-is-it-normally-complicated/

I'd like to applaud the spirit of cooperation evident in this thread.

First please note my very important edit to my post#10. My apologies. There are so many ways to teach electricity but I feel it is important to follow the route that your nephew is following with some extensions if he has the interest. Too many traditional physics texts start with a whole list of declarations which are only semi connected and appear to serve no real purpose. To be studying parallel circuits at 13, perhaps your nephew's syllabus starts somewhere to provide a real motivation. That would be good. But whatever you do, my advice would be to avoid Horowitz.

This doesn't describe a wave it describes either a wavefront or a soliton pulse. For many purposes spherical waves can be approximated by plane waves. This was part of the reason for my original response. Many useful simplifications have been developed over the years. I specifically said I was not initially interested in the nature of the wave from this point of view.

I see that several responders here are also involved with this thread about explaining to others. http://www.scienceforums.net/topic/102079-electrical-circuits/ How many are practicing there the methodology they have vouchsafed here?

The very first thing you need is to decide what sort of wave you mean and how to describe it. By what sort I don't mean sound or light or gravity, I mean its geometric distribution in space, in short its 'shape'. Is it 1D, 2D or 3D? Is it plane spherical or what? Clearly (to you I hope) it is a travelling wave since you say it is reflected. Edit A good clear source for the transition from simpler mathematics to tensor methods in this subject is Modern Optics By Robert Guenther pub Wiley.

Please try to answer any questions like this. They are designed to help understanding as well as resolving an immediate issue. They were written in anticipation of this question for instance Please also note that placing theoretically perfect voltmeters and ammeters in the circuit does not change any real circuit values. At a more advanced level the effect of real world instruments is taught.

The resistance of R2 is independent of any other variable in the circuit. That is it can be set independently of other circuit variables, although there will be a change to currents and perhaps voltages if you do change the value of R2. Please note this is a circuit with all the resistors in parallel. Do you know if this will change the voltage or the currents or both if you change a resistor? Resistors as circuit components are non polarised. That is they can be connected either way round to achieve the same effect.

For future reference. The first thing you need to know is the circuit sign convention. A battery is drawn with the longer of the two lines denoting the positive and the shorter the negative. Conventional current flows from negative to positive. Oops Edit positive to negative (There was recently an ill advised movement to change this convention which still causes much confusion to many people). (Edit serious confused me anyway) You circuit is drawn (thankfully) using conventional current so the readings on the ammeters are positive when convention current flows (from positive to negative through them). The next thing to note is that all the battery current flows through ammeter 5 and since it has no other path from the negative to the positive the current in A5 must equal the sum of the currents in all the available paths from negative to positive. It is quite simple in this case to see that this is equal to A1 + A2 + A3 It is also fairly obvious that the only way current can flow through A2 and A3 is what is left after A1 has left the main flow. ie the current through A4 = A2 + A3

Yes, that's right the derived function is f'(x).

Michel please note you have reproduced the only correct part of my post. This part did not involve the median in any way. It simply points out that if the altitude runs from A to BC ie if E lies between B and C as stated Then angles B and C must be acute. The second part of my post was in error since I mixed up the triangles with sides a, b and c and with sides a2, b2, and c2.

What is your definition of f'(x) ? Are you sure the question does not say If f(x) is differentiable at xo then prove that.....etc ? Consider the differentiability of f(x) = |x| and of f(x) =x2 at xo = 0

Here is some information about falling spheres and rates of solution of substances and the equations that govern these. One thing to note is that there may not be a 'closed form' equation that says answer = ....... This is a very common situation in Engineering. We have to home in on the answer via an iterative or graphical process. Please also not the rate of solution rate constant can depend upon the condition of the substance massive, finely divided etc.

Upon re-reading the OP I find the same interpretation as I originally made viz heliocentric v geocentric motion argument applied to the electron/observer system, clearly considered as a miniature Earth/Sun system. This is why I replied as in post#5 clearly identifying and underlining a classical response, but drawing the distinction between this and a quantum response. As a matter of interest do you think a quantum electron changing its energy level by tunneling in a semiconductor without changing its position in the lattice emits EM radiation?

I can't see it. Either something moves from A to B or it does not. If it does then translation is involved, regardless of what else happens. It doesn't really matter whether that something is a blurred wavelet, a quantum particle or something really esoteric.

Is an electron traversing a 'curved path' translating or 'spinning on its axis'?

So are you paying attention now? Think of it this way A negative is the not or negation operator operating on a positive. using any operator is the same as multiplying by something in mathematics. So the negation or not operator operating on say 10 gives not(10) or (-1) x (10) or (-10) If we do this operation a second time that is we negate our original negate we should end up where we started That is (-1) x (-10). this has to be +10 to end up where we started So the product of two negatives is a positive.