# Recent content by Hells_Kitchen

1. ### 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
2. ### 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...
3. ### 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?
4. ### 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
5. ### 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...
6. ### 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...
7. ### Mathemathical Methods to Solve a Physics Problem

Can someone please comment or suggest me if this is a correct solution?
8. ### 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...
9. ### 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!!!!
10. ### 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...
11. ### 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}...
12. ### 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?
13. ### 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...
14. ### 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) =...
15. ### 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!