Recent content by rafaelpol

Homework Statement I am trying to follow a derivation in Jackson - Classical ElectrodynamicsHomework Equations In equation 1.58 (2nd/3rd edition) of Jackson - Classical Electrodynamics he says that by using the fact that \mathbf{\rho} \cdot (\mathbf{\rho} +\mathbf{n})/ | \mathbf{\rho +n|}^{3}...

He is using r = \sqrt {x^2 + y^2+z^2} , and then \frac{\partial r}{\partial z} = \frac{z}{r} = cos{(\theta)}

Homework Statement It is actually not a problem, but a formulation of the electric potential energy in a dielectric medium present in a book, which seems to me as inconsistent with the way it is usually defined in electromagnetism books. I can't see it as a typo or a mistake because the author...

Homework Statement Say I have a sphere at the origin with radius "a". If I am integrating over a region in which r is greater than "a", how can the bounding surface of this volume be the spherical surface? This comes from an explanation in Greiner Classical Electrodynamics, in which he says...

Thank you very much.

Homework Statement I am following a derivation of Legendre Polynomials normalization constant. Homework Equations I_l = \int_{-1}^{1}(1-x^2)^l dx = \int_{-1}^{1}(1-x^2)(1-x^2)^{l-1}dx = I_{l-1} - \int_{-1}^{1}x^2(1-x^2)^{l-1}dx The author then gives that we get the following...

Thanks. I've got the correct result now. However, when this result is added to the Electric field of the dipole computed by the grad of the potential, instead of adding -4*Pi/3 *delta(r) Greiner adds +4*Pi/3 *delta(r). Why, is that? It seems to be a contradiction since if you integrate over a...

Homework Statement Can't get to the final equality ( integral = - 4*Pi/3). Homework Equations \int_V \mathbf{E }dV = - \int_F \frac{_{\mathbf{p}.\mathbf{e_{r}}}}{r^2}\mathbf{e_{r}}r^{2}d\Omega = \mathbf{p}\frac{-4\pi }{3} The Attempt at a Solution Can't find how to get -4Pi/3...

I set it equal to A because I thought about tensors the way one usually talks about vectors which are the sum of their components. From the requirements needed to be a pseudoscalar, the skew-symmetry of the components of the tensor proves it change signs under a parity transformation. Now, is...

Homework Statement Show that in 2 dimensions a skew-symmetric tensor of second rank is a pseudoscalar and that one of third rank is impossible. The Attempt at a Solution A11=A22=0, while A12=-A21, which makes A= A12+A21, which is certainly skew-symmetric, though I am not sure it is...

I found now what was the problem (I made a mistake while calculating the module of C). Thank you very muchl

Homework Statement Find the sum formulas for cosine and sine using vector methods. Homework Equations Suggestion: use the following vectors A= cos xi + sin xj B= cos yi + sin yj C= cos yi - sin yj The Attempt at a Solution I actually solved the question by doing the dot...

Thank you very much for the extra information (tensors are the next topic of my course).

That is exactly the problem. After solving other exercises of the book I found that this is really a notation issue. In order to obtain the correct answer one has to do the dot product of vector U and del, and then operate with the resultant operator in the vector R. The answer is going to be...

Homework Statement Verification of the product U . del (R) = U Vectors are written in bold Homework Equations R = ix + jy + kz The Attempt at a Solution I cannot understand what is going on. If del R is the gradient vector of R, then the problem will be scalar product, whose...