Recent content by math4everyone

Thanks for the reply, but this was just an example. I apologize for not stating the real problem.The real system of difference equations I have is the following $$ \begin{cases} X_j [n+1] = (1-m_j - \theta - \delta N[n])X_j[n]+\alpha X_a[n] e^{-\beta X_a [n]} \\ X_a[n+1]=(1-m_a-H[n]-\delta...

I have a little question. I want to know if there is a process in which I can find equilibrium solutions to some system of difference equations. For example, if I have something crazy like $$\begin{cases} x[n+1]=(x[n])^2y[n]+z[n]e^{-ax[n]} \\ y[n+1]= z[n]x[n]+x[n+1]y[n+1]\\ z[n+1]=...

Homework Statement Homework Equations $$f_X(x)=\lambda e^{-\lambda x}$$ $$F_X(x) = 1-e^{-\lambda x}$$ $$\mu = \frac{1}{\lambda}$$ The Attempt at a Solution a) $$f_{X,Y}(x,y) = f_X(x)f_Y(y) = \frac{1}{800} e^{-\frac{1}{800}x} \frac{1}{1000}e^{-\frac{1}{1000}y}$$...

I would say it's the same as i1 because it's the same current that flows through the resistors.

Yes:

I think they are equal

Homework Statement I have the following circuit What is the relation between $$I_{eq}~~and~~ i_1, i_2, i_3$$? Homework Equations Kirchhoff Laws The Attempt at a Solution See the image above

Using the fact that $$d\vec{A}$$ is $$\rho d\rho d\phi \hat{\rho}$$. First, I want to calculate the flux in the bottom and top of the cylinder, and I expect it will be slightly similar in the case of the sides. What I want to prove is that this flux is equal to $$\frac{q}{\varepsilon_0}$$

Homework Statement What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way) This is what I have done so far: Homework Equations $$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...

Well, since the field lines with the image charge resembles ellipses, I could guess that it could be half part of an ellipsoid...

Could it be a paraboloid?

I don't know. What I thought was that I can make the height of the cylinder even larger in order to cover those field lines you mention because it doesn't affect the result. And the horizontal field line starts bending in the instant it is coming out the charge, so... I really don't know.

Hello, I tried to do something like this http://imageshack.com/a/img921/9379/gQAcim.png I also thought of doing something with the image charge http://imageshack.com/a/img924/2415/9XBrlC.png However, I am not sure what is the charge enclosed in this sphere...

Homework Statement Homework Equations The z component of the field: $$E_z = \frac{-Qh}{2\pi\varepsilon_0 (r^2+h^2)^{\frac{3}{2}}}$$ The Attempt at a Solution I tried to choose a cylinder for my Gaussian surface such that the radius of it matches with the distance d I am trying to find and...

I am stuck with this problem: The right triangle shown with vertex P at the origin has base b, altitude a, and uniform density of surface charge σ. Determine the potential at the vertex P. First find the contribution of the vertical strip of width dx at x. Show that the potential at P can be...