Recent content by cianfa72

You mean the group homomorphism that map a translation + rotation (i.e. an element of ##E(2)##) to the corresponding element of ##SO(2)## that represent the "rotation part" of the translation + rotation.

Just to check my understanding: elements of ##E(2)## group of Euclidean plane isometries consist of: translations, rotations and composition of translations + rotations. One then can show those elements form a group w.r.t. the composition operator (in dimension 2 it should be...

I would add that the 2nd postulate of Einstein's SR is actually two folded. Namely in any inertial frame: the (two-way) speed of light doesn't depend on source motion, is isotropic (as MMX experiment shows) and has the same invariant value ##c## there exists a consistent way to synchronize...

The above questions arise from a basic doubt about how to use Maxwell's equations in any specific scenario. From my textbooks, Maxwell's equations are solved by taking the sources ##\rho## and ##J## as assigned/fixed functions of spacetime coordinates. On the other hand, EM fields act...

Ok, so in ##(x,y)## coordinates it is $$K_1^{'}=K_1, K_2^{'}=K_2,K_3^{'}=K_3 + 3K_1 - 2K_2$$ One can extend it to any dimension provided that the space is maximally symmetric.

Suppose the point Q has coordinate ##(2,3)## in the given cartesian coordinates. How does one write a set of KVFs that includes the rotations about Q (staring from the KVFs in post#1 and using constant coefficients) ?

Consider ##\mathbb R^2## as the Euclidean plane. Since it is maximally symmetric it has a 3-parameter group of Killing vector fields (KVFs). Pick orthogonal cartesian coordinates centered at point P. Then the 3 KVFs are given by: $$K_1=\partial_x, K_2=\partial_y, K_3=-y\partial_x + x...

When it comes to energy balance, assuming wires with infinite conducibility, one can consider a closed surface around the resistor (load). In stationary conditions EM fields do not change in time, therefore the EM energy stored in the volume enclosed from that closed surface doesn't change in...

Ok, the charge density ##\rho## inside the wire you were talking about is the Type-I surface density as described in the aforementioned paper. We said they are not bound charges (zero polarization inside the wires) therefore I believe they actually correspond to a deficit (positive) or excess...

I would says C) since ##F_n## and ##-F_n## are a Newton 3rd pair.

Ah ok so, wherever the conductivity changes through the wire, where the non-zero free charge density ##\rho## comes from (as you said the polarization ##\vec P = 0##) ?

Therefore in a sense the charge density inside in the wires (wherever the conductivity changes) is actually a bound charge density ##\rho_b## - is it a surface or volume charge density ?

In stationary conditions, however, the non-zero charge density ##\rho## inside the wires (wherever the conductivity change) is constant w.r.t. time. Hence from continuity equation one gets ##\nabla \cdot J = 0##, i.e. the density current is the same along the wires. Here the point is, even...

As said before, the body weight measured by the scale (the body standing still on it) is one of the Newton 3d pair.

Isn't the above in post#45 just a restatement of twin paradox or "differential aging" ?