Recent content by S. Moger

Homework Statement Evaluate \int_C \vec{F} \cdot d\vec{r} Where \vec{F} is the field generated from a circular thread of radius b in the xy plane, with magnitude j in the direction \hat{\varphi} (i.e. not along the curve, I take it) C: (x,y,z) = b(1+ \cos{\alpha}, 0, \sin{\alpha}) 3. The...

Thanks I can show it by evaluating the cases x>0 and <0 separately. B' = B and if rho=q , A = A'+ 1/2 q . But how did the book arrive at that particular formulation. There must have been some other kind of approach to the problem?

Here, \Theta(x) is meant to be the Heaviside step function. When I integrate delta from a to x, there are three cases. x < a, a \leq x<0, a<0 \leq x. For x less than 0, I should get a zero, and for x greater than or equal to zero I should get a 1 from the definition as the 0 is inside the...

Can I actually write like this? \Delta \phi = - \rho \delta(x) if I treat rho as a constant? Wouldn't it be more correct to write an integral containing delta there to avoid the infinity problem there? Anyway, \Delta \phi = - \rho \delta(x) \int_a^x\Delta\phi(u)\,du= - \rho...

Homework Statement Solve the poisson eq. on R with a source in x=0. The Attempt at a Solution I haven't done this kind of thing in years, so I'm a bit rusty, but I think that this is requested: \Delta \phi = - \rho \delta(x) (Edit: no wait, I need an integral here). It doesn't seem to be...

I'm trying a different approach now, The field \vec{F}(\rho, \varphi, z)=F_0 \frac{a}{\rho} (\hat{\rho} - \hat{\varphi}) + F_0 (\cos\varphi \hat{\rho} - (\sin\varphi + \frac{\rho}{a})\hat{\varphi}) Integral of the singular part: a F_0 \oint_C \frac{1}{\rho}(\hat{\rho}-\hat{\varphi}) d\vec{r}...

Yes ok, a paraboloid of revolution. I've tried a couple of approaches, but they all seem to result in a mess. I've transformed the expression of the field to cartesian coordinates to perform the dot product with dr in the same system (or is this unnecessarily cumbersome?) \vec{F}(x,y,z) = a...

Well, it's physics friday! (carpe diem etc, what else) :) 1. Homework Statement I present to you this (not so) pleasant expression that seemingly appeared on a page out of nowhere. \vec{F}(r, \theta, \varphi) = \frac{F_0}{ar \sin\theta}[(a^2 + ar \sin\theta \cos\varphi)(\sin\theta \hat{r} +...

Thanks, that's a very clear and nice explanation.

Homework Statement M= \begin{pmatrix} 2 & -1 & 0\\ -1 & 2 & -1\\ 0 & -1 & 2\\ \end{pmatrix} Compute \frac{1}{6}\epsilon_{ijk}\epsilon_{lmn} M_{il} M_{jm} M_{kn} . The Attempt at a Solution I computed the result which is 4, by realizing that there are 36 non-zero levi-civita containing...

Thanks, it's a bit tricky, but I think I get this part now. It's probably a good idea to write it out in sums like you do, at least at the moment. I get K=2, which will lead the the correct result.

Ok, Would this be a correction? A_{ij} A_{ij} = k \epsilon_{ijk} a_k \cdot k \epsilon_{ijn} a_n Meaning I need to find \epsilon_{ijk} \epsilon_{ijn}? It seems like n \neq k terms amount to zero, because it implies that there's a duplicate index number in one of the levi-civitas, leaving only...

I'm new to working with tensors, and feel a bit uneasy about the nomenclature. I picture words like antisymmetry in terms of average random matrices where no symmetry can be found at all. However, if I understand it correctly, antisymmetry is a type of symmetry, but where signs are inverted. So...

Thanks for your input, I will get back to this as soon as I can !

Ok, you throw a pair of dice and sum the result. In many cases it ends there. However, if a dice shows a 6 it's rerolled after adding a five (not a six) to the sum. The new value of the new roll is added to that sum. So for example: Roll 1: Dice show 2, 3. Result is 2+3 = 5. Roll 2: Dice show...