Recent content by tstin

If z is a complex number, then z=z_{1}+iz_{2} and its complex conjugate is z^*=z_{1}-iz_{2} Then it is easy to prove z+z^*=z_{1}+iz_{2}+z_{1}-iz_{2}=2z_{1} and from this is is obvious that z_{1}=\mbox{Re}\left(z\right)=\frac{z+z^*}{2} Similarly, z_{2}=\mbox{Im}\left(z\right)=\frac{z-z^*}{2}...

That's right... essentially, what I described above is the same as calculating the Jacobian, which is the matrix given by TAMEPLAH. A more rigorous description of coordinate transformations would involve a discussion of Jacobians and why they work and stuff... that's for whoever's feeling...

This is wrong, of course. There's no nice Gaussian surface one can draw to calculate the electric field due to a ring of charge. We can only analytically calculate the field along the ring's axis. Here's an http://www.physics.buffalo.edu/~sen/documents/field_by_charged_ring.pdf" trying to...

This was an old qual problem I was just looking at. Let me describe how to solve it, and then ask another question I had that my solution doesn't answer. According to Lenz's Law, (or really to Maxwell's equation \vec{\nabla} \text{x} \vec{E} = -\frac{\partial{\vec{B}}}{\partial{t}}), the...

Thanks for the LaTeX help, but note that the r's cancel in the \hat{\theta} component of the final solution because the \hat{\theta} component of the gradient in spehrical coordinates has a 1/r in it already. So the last line should read \nabla z = cos(\theta) \hat{r} - sin(\theta)...

This is a problem I have seen a lot on the internet, and no one seems to know what the asker is talking about. We want to know how to express the CARTESIAN unit vectors \hat{x}, \hat{y}, \hat{z} in terms of the spherical coordinates r, \theta, and \phi and their respective unit vectors. The...