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    Helping students transition from High School to University

    I am in the rather unique and exciting position of being able to design an extension curriculum for some gifted Physics students who are in their final year of high school. The goal of the curriculum is to help prepare them for university physics with tools and ways of thinking, without just...
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    Snell's law question with a twist...

    Thanks! I can see now that as the ring falls deeper, the angle light from the ring makes with the boundary between the two media approaches 90, and therefore the angle that the light ray makes with the other side of the boundary approaches the critical angle.
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    Snell's law question with a twist...

    Homework Statement https://gyazo.com/f8cf156e7bd2f2511e3fa859e3732fe6 Homework Equations Snell's law. The Attempt at a Solution I'm mostly confused about the relevance of the second medium (of index n2) given that the distance between the ring and the boundary is "small". Having attempted to...
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    Studying Share self-studying mathematics tips

    Hi all, I'm a physics graduate now working as a maths and physics teacher in a sixth form college. I loved my degree, though wish I'd had the work ethic I do now when I was studying full time. I took a theoretical physics course in my 4th year (syllabus here...
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    Springs in Series & Parallel

    What OCR wants to get at is that if you have a wire of some dimensions, doubling the length halves k without affecting YM, and having two wires (effectively doubling the cross sectional surface area) doubles k without affecting the YM. This lets you nicely draw a distinction between the YM of a...
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    What happens when a particle and an anti particle collide

    That's precisely the point I was trying to make.
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    What happens when a particle and an anti particle collide

    The technical difference between virtual and real particles is that virtual particle are "off shell" meaning that their mass energy and momentum does not satisfy the relation E^2 - P^2 = M^2, however virtual particles should be thought of as a sort of mental abacus that help us calculate things...
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    What happens when a particle and an anti particle collide

    I'd be fascinated to know how one could estimate the volume of matter in the universe without using the method I outlined above. I'd also be interested to know how you came up with that percentage.
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    What happens when a particle and an anti particle collide

    Scientists have indeed, and you're thinking along nearly the right lines: cosmological observations allow scientists to make a reasonable estimate of the energy density of matter in the universe, and calculating the volume of the observable universe is straightforward (though interestingly, due...
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    What happens when a particle and an anti particle collide

    "I think it's possible in principle - just very very difficult." very very difficult is an absurd underestimate. Producing and containing 1kg of antimatter is "possible in principle" in the same way that counting every particle in the observable universe is "possible in principle".
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    Resistance of a wire with changing radius

    R =\frac{x \rho}{A}=\frac{x \rho}{\pi r^2}=\frac{x \rho}{\pi a^2 e^{2bx^2}} Are you sure your expression for dR is correct?
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    Muonic hydrogen, change in potential of the muon.

    Thanks. That makes sense.
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    Resistance of a wire with changing radius

    Remember that A is a function of r when you try to work out dR
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    Muonic hydrogen, change in potential of the muon.

    Homework Statement Taking the proton to be a uniformly charged sphere of radius 1 fm, find an expression for the change in potential experienced by the muon as compared with that in the case of a point-like proton. Use first order perturbation theory to calculate the ground-state energy...
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    * * (Exam tomorrow morning!)

    *URGENT* (Exam tomorrow morning!) Calculating a real integral using residue theorem Homework Statement See attached picture http://imageshack.us/photo/my-images/827/unledozs.jpg/ Homework Equations The Attempt at a Solution Parts a) and b) are straightforward. For b) I end up...
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    Eigenvalues of a matrix B= f(A) given eigenvalues of A

    This looks interesting but i'm having quite a lot of trouble following your notation. Do you know the name of the theorem so i could look it up perhaps? Thanks for the help.
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    Pauli spin matrices, operating on |+> with Sx

    I think I understand where I've gone wrong now. The problem is in my intuition, not in my appilcation of the pauli matrices. as |+> = \frac{1}{\sqrt{2}}(|+_x> + |-_x>) (where |+_x> and |-_x> are the eigenvectors of S_x with eigenvalues +/- 1/2) when we operate with Sx we obtain...
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    Pauli spin matrices, operating on |+> with Sx

    Homework Statement What is the result of operating on the state |+> with the operator Sx? here, |+> denotes the eigenstate of Sz with eigenvalue 1/2. I am working in units where h-bar is 1 (for simplicity, and because I don't know how to type it) Homework Equations S_i = \frac{1}{2} σ_i...
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    Eigenvalues of a matrix B= f(A) given eigenvalues of A

    Homework Statement Find the eigenvalues/vectors of A. (I can do this bit :P, A is a 3x3 matrix) What are the eigenvalues and eigenvectors of the matrix B = exp(3A) + 5I, where I is the identity matrix? Homework Equations The Attempt at a Solution I have (correctly) found that A...
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    Deriving an expression for internal energy.

    Ah of course! Thanks very much for your help.
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    Deriving an expression for internal energy.

    Doesn't this only hold for a reversible process?
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    Deriving an expression for internal energy.

    Homework Statement Show that the change in internal energy of a simple system between states (V1, T1) and (V2, T2) is given by ∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dV Homework Equations dU=dQ-pdV The Attempt at a Solution As U is a function...
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    Uncertainty calculation for calculating pi using Monte Carlo integration

    Bear in mind that this is the only method mentioned above which doesn't require you to already know the value of pi.
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    Delta/Heaviside Functions

    You have the correct shape, however you may define a value at x= 0, 1, 2 for the heavside step function. Personally I think 1/2 is the most sensible, because it means that the function is odd and the approximation H(x)={1+tanh(kx)}/2 holds exactly in the limit k->infinity. 0, 1 and 0.5 are all...
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    Delta/Heaviside Functions

    should make it a bit easier to read, can't get your array to work though.
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    Complex functions, (z+i)^5 + (z-i)^5

    thanks, that's quite a lot neater.
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    Complex functions, (z+i)^5 + (z-i)^5

    yes, exactly that.
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    Scaling Property of the Dirac Delta Function

    I *think* it's because you're redefining u->t. Normally when using a substitution you just either substitute back in at the end or change the limits over which you are integrating. If you redefine u so it is a times smaller than it was before, you also need to make sure all the constants are...
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    Complex functions, (z+i)^5 + (z-i)^5

    Homework Statement solve (z+i)^5 + (z-i)^5 = 0 Homework Equations The Attempt at a Solution I have found the five possible values for z by expanding the original expression into powers of z and i. The imaginary terms cancel exactly, leaving a cubic equation in z which is easily solvable...
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    Thermodynamics: The principle of equal (a priori) probabilities

    I *think* the question is asking "should the probability of the system being in a particular configuration be the same as is stated in PEEP" but that doesn't seem right. Is there a typo in your version of the question? It's very hard to understand what you're being asked for.
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