Recent content by Emanuel84

I finally realized Mathematica didn't do all the simplifications! :smile: By using Simplify command it comes up that curl(E)=(0,0,0) even in cartesian coordinates, as it should be. Thank you, anyway!

Here is a quick computation I made with Mathematica regarding this problem. As you can clearly see, in one case the curl is 0, in the second one is different from 0.

Homework Statement Since the electrostatic field is conservative, show that it is irrotational for an electric dipole, whose dipole momentum is p .Homework Equations \nabla \times \mathbf{E} = 0 The Attempt at a Solution I know that the components of the electric field in spherical...

Thank you, I solved the problem...it was a banal error sign, as you said. :-p

This is quite straightforward. Let's start with: M\vec{R} = \sum_i m_i \vec{r}_i Square it: M^2 R^2 = \sum_{i,j} m_i m_j \vec{r}_i \cdot \vec{r}_j \qquad (1) Then consider \vec{r}_{i j} \equiv \vec{r}_i - \vec{r}_j \Longleftrightarrow r^2_{ij} = (\vec{r}_i - \vec{r}_j)^2 = r^2_i - 2...

On the other hand, one can think to use the definition of canonical trasformation: A time-independent transformation Q = Q(q,p) , and P = P(q,p) is called canonical if and only if there exists a function F(q,p) such that: dF(q,p) = p_i dq_i - P_i(q,p) dQ_i(q,p) In other words...

I know that: [Q_j, P_k] = \delta_{jk} so, in this case, since Q = Q_1 and P = P_1 , we have: [Q_1, P_1] = 1 = [Q, P] These are the calculations I made: [Q,P]_{q,p} = \frac{\partial Q}{\partial q}\frac{\partial P}{\partial p}-\frac{\partial Q}{\partial p}\frac{\partial P}{\partial...

err...how can I deduce momentum and energy? I didn't study Noether's theorem yet, so I don't think this problem should use it... :redface:

Hi, I tried to solve this problem, but I was unsuccessful Here is the problem: Given the transformation: \left \{ \begin{array}{l} Q = p^\gamma \cos(\beta q) \\ P = p^\alpha \sin(\beta q) \end{array} \right. a) Determine the values of the constants \alpha , \beta and \gamma...

Thank you everyone! :approve:

Hi, I'm wondering how to prove the following...can you help me? :redface: F^{\mu \rho} G_{\rho \nu} = \eta^\mu_{\phantom{\mu}\nu} \mathbf{E} \cdot \mathbf{B} F^{\mu \nu} F_{\mu \nu} = -2\left(\mathbf{E}^2-\mathbf{B}^2\right) G^{\mu \nu} F_{\mu \nu} = -4\,\mathbf{E} \cdot \mathbf{B} G^{\mu...

Is someone able to proove the invariance under Galilean transformations of F=dp/dt within a system of variable mass? In particular is the momentum invariant? i.e. p=p', as Goldstein states? Please answer me! :wink: