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    Mathemathical Methods to Solve a Physics Problem

    \frac{\partial^{2}V(x,y)}{\partial (x^2)} + \frac{\partial^{2}V(x,y)}{\partial (y^2)} =0 \frac{\partial^{2}V(u,v)}{\partial (u^2)} + \frac{\partial^{2}V(u,v)}{\partial (v^2)} =0
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    Mathemathical Methods to Solve a Physics Problem

    Can someone please suggest how to solve this problem. The above solution is not correct because apparently it assumes that the potential along the x=0 and y=0 planes is constant but it is not. It is only constant at the boundries around the circle as described above. Here is the hint that we...
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    Mathemathical Methods to Solve a Physics Problem

    cazlab, thanks for you suggestion but I think I HAVE TO solve it with conformal map transformations. Can someone else please suggest a solution or a comment on this exisiting solution?
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    Series Summation Convergence

    Sorry I had a mistake for the n=0 term. I took it to be 1/2 instead of 1. here is the corrected version. The integral now becomes: \int\frac{2\cos{x}-1}{5-4\cos{x}}dx=\tan^{-1}(3\tan\frac{x}{2})-\frac{x}{2} Again using mathematica
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    Series Summation Convergence

    SammyS, I think your suggestion with the S'(x) was genius. Here is what I got for final result. Can you please check me? I'm stuck now with finding an analytical solution to: \int\frac{3}{10-8\cos{x}}dx but I solved in mathematica and it gives: \tan^{-1}(3\tan\frac{x}{2}) Any...
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    Series Summation Convergence

    If it is not of too much trouble can you please expand on your answer a little further. Do you think there is a way to convert this into. \sum_{n=1}^{\infty}f(x)g(x) =\sum_{n=1}^{\infty}f(x) *[]= \frac{2sin(x)}{5-4cos(x)} *[] and consider f(x)=\frac{sin(nx)}{2^n}. Finding the [] then would...
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    Mathemathical Methods to Solve a Physics Problem

    Can someone please comment or suggest me if this is a correct solution?
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    Mathemathical Methods to Solve a Physics Problem

    Homework Statement An infinite hollow conducting cylinder of unit radius is cut into four equal parts by planes x=0, y=0. The segmments in the first and third quadrant are maintained at potentials +V_{0} and -V_{0} respectively, and the segments in the second and fourth quadrant are maintained...
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    Series Summation Convergence

    Please also find the attached document for full derivation so far. I am stuck with the \frac{1}{n} term. Can someone please suggest a solution or help. Thank you so much!!!!
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    Series Summation Convergence

    HallsofIvy, I am sorry if I was a little misleading. The problem is simply to find the sum. The second part of the problem is actually to plot the answer that we find as a function of x and the sum of the first five terms for n=1,2,3,4,5 in the interval -5<x<5. I think the idea is to compare...
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    Series Summation Convergence

    By the way the result given above by expressing \sin(nx)=\frac{\exp(inx)-\exp(-inx)}{2i} Then I applied the geometric infinite series for the \frac{\exp(ix)}{2} to the n-th power and \frac{\exp(-ix)}{2} to the n-th power. Doing some algebra we get that \sum_{n=1}^{\infty}...
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    Series Summation Convergence

    Find the convergent sum and find the sum of first five terms \sum_{n=1}^{\infty} \frac{sin(nx)}{2^nn} from 1 to infinity. I have found so far that: \sum_{n=1}^{\infty} \frac{sin(nx)}{2^n} = \frac{2sin(x)}{5-4cos(x)} I am not sure how to consider the \frac{1}{n} term. Can someone please help?
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    Particle Pair Annihilation

    No. They're my questions, the answers of which I think are an attempt to better answer the "Why or Why Not" part of the problem. It makes sense that the initial momentum before collision would be zero: p_initial = mv/(1-v^2/c^2) \hat{x} + mv/(1-v^2/c^2) \hat{-x} = 0 p_final of the photon may...
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    Particle Pair Annihilation

    1. Problem Statement What is the wavelength of each of the two photons produced when a particle pair of a positron and electron accelerated at 25GeV collide? Can the net result of this annihilation be only ONE single photon? Why or why Not? Homework Equations Etotal(initial) =...
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    Moment of Inertia: Solid Sphere

    I understand! r_{\perp} = rsin{\theta} Then you get \int^{\pi}_{0} sin^3{\theta} d\theta , which is just \frac{4}{3} using sin^3{\theta} = sin{\theta}(1-cos^2{\theta}) identity and it works out to be I = \frac{2}{5} MR^2. Thanks!
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    Moment of Inertia: Solid Sphere

    How come when you use this we get: I = \int r^2dm = \rho\int^{2\pi}_{0}d\phi\int^{\pi}_{0}sin{\theta}d\theta\int^{R}_{0}r^4dr = \frac{3M}{4\pi R^3}*2\pi*2*\frac{R^5}{5} = \frac{3}{5}MR^2
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    Help with 2 problems about compact/pointwise convergence from Munkres - Topology

    Hi everyone, I am stuck with 2 problems from Munkres' book and I would appreciate if someone helped me solve them. Thank you in advance. Here they are: 1. Consider the sequence of continuous functions fn : ℝ -> ℝ defined by fn(x) = x/n . In which of the following three topologies does...
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    For loops in Matlab

    Yeah, I absolutely agree it is definately easier to do hc_found = a and that is what I did at the end. I just wanted to show that that's what happens when you don't know what you're doing. You end up typing 150 times the same thing for something that you just need to type one letter...
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    For loops in Matlab

    Hahaha and I just finished typing up 150 values. Thank you so very much for your answer though. Do you know, if I want to do a 3D plot of hc_found, gamma and a different range of x_inf how would i be able to do that. It tells me that one of these has to be a matrix. hc is implicitly...
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    For loops in Matlab

    Right sorry I didn't explain that really well. I meant if i replace final_result(i) = hc_new; with final_result(150) = hc_new; inside the code. Otherwise you are right I can access each point individually from the results of the loop. Please look at previous post Many thanks, HK
  21. H

    For loops in Matlab

    I found that if I do the following I get the right datapoints I need and the correct graph: %Range of gamma gamma_range = [0.01:0.01:0.5]; hc_found =...
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    For loops in Matlab

    I figured it out for the zero parts. Apperantely MATLAB can create the array itself and it does need this line of code: final_result = zeros(150) You don't need to intialize an array of zeros I guess even though I would have thought that you needed to. Now the loop runs fine but it has this...
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    For loops in Matlab

    No, of course the C and b are being calculated beforehand. Here is the total code. Maybe you can run it yourself and see what it produces. I am getting just 150 zeros for final_result(i) I need a graph of final_result array versus gamma_range array. Many thanks for all your efforts. -HK...
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    For loops in Matlab

    This didn't work. It just gave me 150 zeros. I don't know why because theoretically it does make sense. But thank you for your effort. :) Plus there is another problem here, I think when the for loop takes a 1 it calculates gamma as 1/150 = 0.006666 and it should be 0.01 and so on for the...
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    For loops in Matlab

    Hi Thank you very much for your help it was really helpful and I think I got the most important part to work. Sorry to bug you but just one more quick thing. This is what I have so far. I just need to be able to plot final_result versus gamma_range. But do you know how I can store the values...
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    For loops in Matlab

    Thanks for your response but could you explain a bit more "further calculations part". And a little more detail of the overall code if you don't mind. I am doing some research with a professor and we have this equation which cannot be solved directly because it is implicit. hc =...
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    For loops in Matlab

    Thanks for your advice but I'm still not quite clear what you mean. A while loop seems to be a better idea here. But how would I translate the following in code: while hc(n) - hc(n-1) < 0.001 end otherwise continue until hc(n) - hc(n-1) <0.001 print (hc(n)) Thanks
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    Engineering Calculating the Effect of an Electrical Short or Open on a Series Circuit

    In addittion to what was said I would add a couple of comments that might not answer your question directly but are useful to know when analyzing these problems. 1. Remember that the current always takes the path of the LEAST resistance. 2. Resistors cannot short a circuit because there...
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    For loops in Matlab

    Homework Statement Can someone help me set up a "for loop" for this equation I intialize hc = x0 then I have to compute hc1 = C.*(log(hc./b)+1)+ gamma.*(1-exp(-hc./gamma)) hc2 = C.*(log(hc1./b)+1)+ gamma.*(1-exp(-hc1./gamma)) hc3 = C.*(log(hc2./b)+1)+ gamma.*(1-exp(-hc2./gamma)) hc4...
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    Beat Frequency for a Laser!

    Homework Statement A laser emits a monochromatic beam of wavelength \lambda , which is reflected normally from a plane mirror, receding at speed v . What is the beat frequency between the incident and reflected light? I know that the f_{beat} = |f_2 - f_1|. When the wave hits the...
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