Recent content by Vincf

In the reference frame attached to the magnets, the electric field has a conservative circulation, and therefore: $$ \oint \mathbf{E} \cdot d\mathbf{l} = 0. $$ There is indeed an electric field associated with the surface charges distributed along the conductor. However, it cannot sustain a...

The question of whether the Maxwell–Faraday equation plays a role—that is, whether the electric field has a non-conservative circulation—may depend on the choice of reference frame. To avoid issues related to rotation, let us consider a rectangular conducting loop moving at constant velocity...

There is a flaw in my previous argument. Using the impulse response assumes zero initial conditions, in particular that the input vanishes for ##t<0##. However, the regularization I introduced does not satisfy this, since ##e_a(t)\neq 0## for ##t<0##. Therefore the relation...

It is possible to see what happens when we replace the Heaviside echelon with a more regular entry. For simplicity, I restrict myself to the case where ##C_1 = C_2## and I consider the differential equation (with ##\tau = RC##): $$ 2\tau \frac{ds}{dt} + s = \tau \frac{de}{dt} $$ The impulse...

I had not understood that the OP was specifically asking for the value at t = 0. In the general case, if one modifies the circuit in any way such that the order of the differential equation on the output side becomes strictly higher than that on the input side, then the output is necessarily...

To be more precise, let me complete the analysis using the Laplace transform, which is very straightforward since: ##E(p) = \frac{E}{p}## and ##v_s(0^-) = 0## We have: $$ H(p) = \frac{C_1}{C_1 + C_2}\,\frac{p}{p + \frac{1}{R(C_1 + C_2)}} $$ Hence: $$ S(p) = H(p)\,\frac{E}{p} =E \frac{C_1}{C_1...

This is a very classical situation when a Heaviside step is applied to a capacitor, or to an arrangement of capacitors forming a closed circuit in series with the step. The voltage across the capacitor is obviously not continuous in this situation, and an infinite current spike is associated...

Am I missing something? Apart from scenario 2, in which the system is moved as a whole, are the others not practically feasible?

In continuum mechanics, one defines a mass-specific internal energy density by $$ e = u + \frac{1}{2}\,\rho\,v^2, $$ where ##\mathbf{v}## is the macroscopic velocity of the material element. The total internal energy is then : $$ U = \int u \, dm. $$ A sufficient separation between the...

As previously mentioned in this discussion, "heat" is a mode of energy transfer, and therefore the term "heat" is inappropriate. We should be talking about internal energy. Even the thermal agitation associated with a monatomic ideal gas can easily be exchanged as work with a piston.

I don't know if that answers the question. One possible answer would be that you can convert all the kinetic energy of the "cold" ball into work, whereas you are limited in this conversion by the second law of thermodynamics if you want to use the internal energy of the "hot" ball.

In continuum mechanics, one defines the vector field $$ \boldsymbol{\omega} = \frac{1}{2}\,\nabla \times \mathbf{v}. $$ It measures the local rotation of a material particle. In the case of a deformable medium, this vector field may vary in space. However, a defining property of a rigid...

Your mistake comes from differentiating the dipole moment as well, whereas it must be kept constant during the differentiation. To clearly expose the issue, I will redo the calculation in the simplest possible case: a field directed only along the x-axis (which actually corresponds to your...

I received a warning message about "Unacceptable references or topics." I'm new to this site. Does this mean I have to delete the reference I provided, or all the posts? It's a very traditional French journal aimed at French physics professors. I'm currently retired, and my goal is absolutely...

I prefer to pose the question this way: I have a finite charged plane and a point ##M## above the charged plane at a height ##z## much smaller than the distance to the edge. Does an "infinite plane" model allow me to predict the field at ##M## without worrying about the details of the plane's...