Ah, ok, then I understand it now. I think the first thing I were trying to do was integrating an object, namely the current density J, which is simply everywhere zero except at the boundaries of the cylinder over an area which intersects the current density vector J perpendicular. This cannot...
Ah, so you mean I have to integrate the surface current density K (unit A/m) over the line my curve intersects the cylinder? So I get K*length(curve) = K*L.
Well, I think we can assume the cylinder to be a perfect conductor carrying only a surface charge density at its outside. So inside there will not be any current.
Homework Statement
The problem is to find the magnetic field within a rotating cylinder (infinitely long) that has on its surface a given surface charge density p. I made a picture of the problem to illustrate this. The only hint given: "the magnetic field outside the cylinder is zero...
Homework Statement
Given the function g(x)=e^u(x) where u(x) = -(1-x^2)^(-1). I have to integrate this from -1 to 1.
The Attempt at a Solution
I know the function is symmetric. It is enough to integrate it from 0 to 1 to get the real value of the integral. Well, beside that I have...
I'm so confused because sometimes Steiner's theorem isn't used and sometimes it is used for rolling objects. Can you please generalize, when I have to use Steiner's theorem for rolling objects? Would be really helpful.
Homework Statement
Consider a spere with momenta of inertia of 2/5*m*r^2 that rolls down a plane surface (no friction). I want to calculate the rotational energy of the sphere when it has speed v0.
Homework Equations
Erot=1/2*I*w^2
The Attempt at a Solution
My only problem is: Do...
Sorry, I cannot use this Latex editor.
But you're right, I have to write out the inner product (in reference ot the basis I wrote down) in the matrix version.
Homework Statement
Given the Vectorspace V of the real polynoms and the sub space L(1, t, t^2). On V there's a inner product defined as follows:
<u(t), w(t)> = integral(u(t)*w(t), dt, -3, 3)
I have to find the inner product of the subspace in reference of the basis (1, t, t^2)...
Ok, this way I can solve it easy. It is no problem. I want to try it the other way. I mean, I know the solution of the problem in the frame of the moving particle p0 and want to transform it into the lab system (my system).
Homework Statement
A particle with momentum p0, mass m0 and energy E0 decays into two particles with mass m1 and m2. Find the energy of the particle E1 and E2.
Homework Equations
Four-momentum!
The Attempt at a Solution
I calculated the energy of particle 1 in S' (system where...
Homework Statement
Let F(AB) be the Frobenius-Norm in respect of the matrix A*B. And let ||A||2 be the operator norm. I have to show that
F(AB)<=F(B)*||A||2
2. The attempt at a solution
I wrote F(AB) in terms of sums and then tried to go on. But I don't know how I could include the...
What's the problem with the following. I mean information can not be faster than c. But let's take a massiv disk with radius r and angular velocity 0. If I start giving it angular velocity from the centre then the outer site must also get speed, but in accordance with special relativity the time...
Well, forget the whole thing about Lorentz-transformation. I was driving car today and thought about the very basic principle of a "transformation" and what it really means and applied my insight to special relativity and my question above.
At the very moment I understand the concept. I...
Another question: Let's say I'm an observer in S and there is a system S' moving with speed v relatively to S. Then take an event in S at x=0 that takes 5 ticks. If I transform this with Lorentz-transformation in S' then I get:
dt'=gamma*dt=gamma*5s > dt (For me in S)
Does that mean, that...
Again, something is missleading me. Let's take the following systems: S' system of a muon moving with v, S system earth.
Question How long is the length h (system S) in S':
==> take Lorentz-transformation: dx'=gamma*(dx-v*t)
==> h'=gamma*h which is wrong.
Why should it be h'=gamma^-1*h...
Well, I understand the Lorentz-Transformation and comprehend the principles of special relativity but I'm confused about something very basic.
Let's assume S is a system (inertia) and S' is relatively moving to S with velocity v. Now I can take the Lorentz-transformation to get from S into...
Also think of the following: If there is a constant inside an integral you can move it outside the integral (sorry, don't know this formula editor):
INTEGRAL(c*f(x)dx)=c*INTEGRAL(f(x)dx)
So in your case 4/3 is a constant (independant of x) and you can move it outside the integral, getting...
Mhh, you're right, uff, in my calculation 1^2+1 equaled 3. Uff, well, then I haven't to do the last row seperately. What had my assistent thought if he had seen this misscalculation :).
Thanks
No, if I do that, then all elements of the last row are zero exzept the first one and the last one (because the calculation of the 1x1 element is another one than the one of the 1x2, 1x3, ... element according to the rule the matrix is built). So I end with almost a diagonal matrix (the first...
Ok, I solved it succesfully by transforming it into a triangular matrix. (I multiplied every row with factor (k+1) or something and then substracted the row with the next row). So I got almost a triangular matrix (except the last row). The last row I treated seperately.
Thanks for your help
Homework Statement
Given the following 101x101 matrix: Akl where k and l are the row and column. Now Akl = (akl)=k^2+1 if k=l and (akl)=2*k*l else. I have to calculate the determinant of this matrix but have no clue how to start working, well I've some idea but it doesn't really help...
I know that it isn't elementary, else I had calculated the integral with some method. The task and goal is to estimate the integral of sin(x^2). For example I could find some other function f(x) such that f(x)>=sin(x^2) and with the special property that the integral of f(x) converges, thus...
Well, the areas in further regions of the x-axis get smaller and smaller (sin(x^2)) and in sin(x) the areas are always the same.
Can you give me a hint?
Ok, I've solved it successfully. Thanks.
The next one is to check wheter the integral of sin(t^2) from 0 to infinity is divergent or convergent.
What I did so far is to find the zero points of sin(t^2) which are in (n*pi)^(1/2). So I can write our integral in a new way, more precisely...
Homework Statement
Given the integral f(t)=sin(1/t)dt from 1/pi to infinity. Examine if it is convergent.
Homework Equations
No particular equation. But I know that if the integral of a function g is convergent and there's another function h such that |h|<=g than the integral of h is...
Homework Statement
The problem is quite easy, but I've still trouble solving this.
Given the two base vectors e1=(1,-2,0) and e2=(0,3,0) and the other ones of a different vector space w1=(1,0,0) and w2=(0,1,0).
I've to find a matrix A that that does the following Ae1=w1 and Ae2=w2...
I thought that, too. I mean that it follows imidiately, but our lecturer said that we've to take |f(a)|=<|f(a)-f(y)|+|f(y)| to show that.
With limited in a suitable environment it is ment what you said (bounded in some neightboorhood).
Homework Statement
I've to show that if f:R->R is continuous in x' then f is limited in a suitable environment of x'.
2. The attempt at a solution
My lecturer said we should use the following inequality
|f(a)|=<|f(a)-f(y)|+|f(y)|
But how should I go on, I know I have to show...
But consider f(x)=x. Then f(x)+x^2 has no real minimum and lim f(x)/x^2=x/x^2=1/x=0. So I must show that |f(x)+x^2| has a minimum.
By the way:
HallsofIvy: I understand your explanation but how would you integrate this in a proove of x^2+f(x)>=t^2+f(t) for every x in R?
In theory f(x) could be a function like that one in my picture. I don't really understand what you mean with "bounded". I mean in what case are they bounded?
Homework Statement
Given a continuous function f(x):R->R with
lim(f(x)/x^2)=0, x-->+-infinity
Show that then an element t exist such that:
x^2+f(x)>=t^2+f(t) for every x in R.
Homework Equations
-> The mathematical definition of continuous and limes
(but I really don't know...
A block is accelerated with a, take a look at the picture. There is a friction between the red block and the other one with mass m1. The friction is given by the coefficient u1.
I have to determine a such that the blue block is not moving relative to the red one. a has to bi in depenence of...
Ok, the state psi can be represented as a linear combination of several possible states psi1, psi2. If I understand this correctly.
With the second question I mean this: let's say we have two free electrons described by the wavefunctions psiE1 and psiE2. Now what happens in nonrelativistic...
As I recognised we can't really take a linear combination, as you said ZapperZ. But what is then meant by the different psi's of:
psi = c1*psi1 + c2*psi2 + ...
And another question:
I saw in my textbook that we can describe a many body system like the helium atom with a wave function...
I have a simple question. In quantum mechanics the superposition principle is given:
psi=c1*psi1+c2*psi2+...
Now, is it possible that psi1 is an electron A and psi2 is an electron B? I mean can we bring several electrons in superposition? Couldn't this violate the probability...
Consider the famous experiment of electron diffraction. electrons are accelerated by an anode. After this anode there is a graphit target (to create an interference pattern). In this case one has to take the Bragg condition to calculate the angle constructive interference actes. The Bragg...
Why can then certain materials only absorb light of a certain polarization if the direction of the polarization depends only on the manner one has chosen the x and y axis? (I mean the material does not care about my chose)?
Light can be x- or y-polarized. However, the polarization depends on the direction of the electric field (lets talk only of linear polarization). Now, what's the difference between x and y polarization? I mean why isn't there an intermediate polarization direction. One could rotate the electric...
Elementary quantum mechanics is mostly based on the SCHRÖDINGER EQUATION. So you could take a look on this differential equation. Its fundamental. Then with this equation you should know something about "EIGENVALUES" and quantum mechanical "EXPECTATION VALUES" and "DEFIATIONS" and of course...
The London van der Waals force is approximatly given by F=-c *a^-7 where a is the distance between two neutral atoms and c is something like this:
C=-23*hbar*c/4pi*(alpha1*alpha2)
where alpha1 and alpha2 =(epsilon-1)/(4pi*N)
and N is the atom number density and epsilon the...