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  1. O

    Trouble solving a differential equation

    What about f(x,y) = exp(x)exp(i*y) Then first derivative w.r.t. x is just f(x,y) First derivative w.r.t. y is i*f(x,y) Sum of their squares is zero, yet they are not constant. f is necessarily constant under the constraint that f has first partial derivatives which are functions...
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    Magnetic Field in a Single Current Coil

    I did, but you get this really tricky integral. I was wondering if there might be a smarter way to do it than brute force.
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    Magnetic Field in a Single Current Coil

    I understand that the magnetic field in a solenoid can be approximated as being constant as the length of the solenoid tends to infinity, but I was wondering if anyone could show me or point me in the direction of a derivation of the precise magnetic field at any point within a single loop of...
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    COV area under a curve

    So, If you've got two points and a given length of curve to 'hang' between them, what shape is the curve which minimises the area underneath it? For a curve which is almost the same length as the distance between the points, this would be a catenary, I think (a la famous hanging chain problem)...
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    Ring of light

    Naty1 - I'm not sure this accounts for the ring. Look at http://en.wikipedia.org/wiki/Sun_dog , posted by jmatejka. That seems to match up perfectly with what I saw. The similarities of the visual description I gave to the one in the article is actually quite uncanny.
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    Ring of light

    Thanks, that's pretty interesting.
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    Ring of light

    I was in the French Alps the other day, high in the mountains (not sure if this is relevant), and, on the night of a full moon, with mist in the sky, there was a circular ring of light around the moon. The ring subtended an angle about 5 times that subtended by the moon (that is to say, it...
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    FUNDAMENTALLY RANDOM occurrences in physics.

    I'd argue that, classically, neither turbulence nor brownian motion can be considered fundamentally random. In the classical argument, as long as we know exactly where every particle is at some point, and what it's velocity is at that time, we can predict exactly what will happen, even how...
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    Classic Problems

    I find it very interesting trying to solve the 'classic' kind of physics problems. The ones that Euler, the Bernouillis and co. bandied about, I've come across: The shape of a hanging chain The shape of a hanging elastic string The brachistochrone (the shape of a wire such that a bead...
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    Surface element meniscus - free body diagram

    Incidentally, this treatment predicts that the shape of the meniscus is independant of the ambiant pressure, which I like. It agrees with rater ad hoc experiments I performed with water in a shot glass: covering the glass with my mouth and sucking in to see if the shape of the meniscus...
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    Surface element meniscus - free body diagram

    I think I may have a solution (which might demonstrate to you the problem I had in the first place - I don't think I expressed it particularly well). Far from the edge of the glass, the surface water pressure is zero.' 'Within' the meniscus, the pressure must be negative (pgh and all...
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    Surface element meniscus - free body diagram

    We are, and I've neglected pressure effects in my discussion above - the argument remains the same in a vacuum (I think).
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    Surface element meniscus - free body diagram

    Because (assuming the glass is hydrophilic), the water / glass interface has a lower surface energy than the glass / air interface, so the water 'creeps up' a little to minimize the energy. It's the same as saying the water's surface tension pulls it up the wall.
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    Surface element meniscus - free body diagram

    That's the thing, though, I think there would have to be a meniscus in a vacuum. The water would still 'creep up' the side of the tube to reduce the surface energy. Wouldn't it?
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    Surface element meniscus - free body diagram

    In a vacuum, though, the pressure in the water cannot be lower than the pressure outside it. that was what puzzled me.
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    Surface element meniscus - free body diagram

    Studiot, I'm not conviced by your treatment of the meniscus. In a wide beaker, where the surface curvature is zero in most places, some column of water is clearly not held up by the surface interactions, but rather by the normal force of the bottom of the beaker, I would suggest that this is the...
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    Surface element meniscus - free body diagram

    Andy - my problem is in your second sentence. In the water droplet diagram provided by studiot, the curvature clearly counteracts the pressure drop. The water is of a higher pressure than the air around it (or the vacuum in the example given). In the meniscus example, the water surface curves...
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    Simple Question(s) About Angular Momentum

    If you apply an impulse (magnitude I) to a pencil, the net linear momentum of the pencil must increase, according to Newton's third law, wherever the impulse is applied. In the example, we push the end of the pencil. The impulse acts along a line perpendicular to the pencil. Taking moments...
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    What happens when two masses touch?

    Thanks, sorry. History a little shaky.
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    Surface element meniscus - free body diagram

    How do you get pics online? Nicely explained. Look forward to your next post.
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    What happens when two masses touch?

    It's a question that simply cannot be answered by classical physics. It was a big problem in the 19th Century that contemporary theory suggested that the most energetically favourable configuration of charged particle would be 'all on top of each other'. It was only when Heisenberg came...
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    Surface element meniscus - free body diagram

    We are considering a jug of the stuff. Apologies - the droplets were a separate thought illustrating a point - that we could forget about boiling. Here are the conditions: We are interested in the profile curve of a liquid at a solid - vacuum boundary (say a water meniscus in a test tube...
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    Surface element meniscus - free body diagram

    I don't think so. Effect of evaporation and boiling, I think, can be ignored. Consider a water droplet in a vacuum - really it would boil away. However, we can still model a non-boiling stable droplet, where the fluid pressure in the droplet equals the net inwards 'curvature force' due to...
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    Surface element meniscus - free body diagram

    Agreed, but it acts on a surface element in the same direction and the net curvature force due to surface tension - away from the water (towards the vacuum) - along the normal of the element. How are these forces balanced?
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    Hot objects

    And less relevantly, but equally interesting: If you hadn't heard of him, Feynman was one of the great physicists of the 20th century, and won a Nobel Prize for his work on quantum mechanics, so a reliable source!
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    Surface element meniscus - free body diagram

    Consider the free body diagram of a surface element of a water - glass meniscus in a vacuum. Along the line normal to the surface, the water pressure acts towards the vacuum, and the direction of the surface tension 'curvature force' depends on whether the surface curves like a 'u' or like an...
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    Start from the Action

    I was struggling with the same problem, and think I have some sort of a remedy. In deriving the E-L equations, by varying a path and evaluating the stationary point of action, it is true that start and end points (define point: time and place) are set. However, it is equally relevant that these...
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