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...
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?
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) =...
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...
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...
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...
Hi there,
i was wondering if you had any thoughts on the following question:
Let (a_{1}, a_{2}, ..., a_{2n}) be a permutation of {1, 2, ..., 2n} so that |a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}| , whenever i \neq j .
Show that a_{1} = a_{2n} + n, if 1 \leq a_{2i} \leq n for i = 1,2, ..., n
I am trying to solve the following linear program using the tableau method:
Max Z = 25X1 + 100X2 subject to:
0.10X1 – 0.90X2 + S1 = -10
0.85X1 – 0.15X2 + S2 = -15
0.60X1 + 0.60X2 + S3 = 40...
Homework Statement
Suppose you have the density of a disk given by σ=σ0*rn.
For n approaches infinity, find the limit of M.I. Interpret your result, which should be physical, reasonable and intuitively clear.
Homework Equations
Now i found the moment of intertia of the object to be...
Could someone please explain the difference between Perfect Diamagnetism and Superconductors in terms of the Meissner Effect and the magnetic field passing through an element of the sort.
Under low temperatures in perfect diamagnetic materials if there is a magnetic field it remains the same...
A confusing trigonometric question!!!
Hi guys, I had a question. I was given the following equality. There was no problem statement that came with it (i.e. it did not say solve the equation or prove the identity, or anything of this nature)
sec x + csc x / tan x + cot x = sin x + cos x...
Homework Statement
I am having trouble with an E&M conceptual problem. Suppose we have two sheets of infinite charge, one positive and one negative (the positive is left of the negative and they have charge densities given respectively alpha and - alpha.). The problem asks to find the...
Hi there can someone help me on this one:
If gcd(a,b)=1 then gcd(a,bk) = gcd(a,k)
I have arrived at the conclusion that gcd(a,bk) gcd(a,k) both divide k but from here I do not get anywhere.
I would like some hints on this please.
Here is the catch:
We are given a 2-D velocity flow incompressible, irrotational of the form:
--> ^ ^ ^ ^
V = u i + v j = [4y -x(1+x)] i + y(2x+1) j
and we are asked to find the flow potential which obeys the Laplace Eq. for 2-D...
The problem is the following:
I need to find the mass, moments along the axis and the center of mass of the tetrahydron (centroid) with vertecies (-1,0,0) (1,0,0) (0,1,0) and
(0,-1,0) and (0,0,2) basically it has a square base with an area of 4 and height 2 units.
You are also given the...