Another thing: in two dimensional Maxwell equations, the equaions (4) are equal to unknowns (4: Bx By Ex Ey).
From 2D->3D, only curl equations increase, while divergence not.
Therefore, I think the explanation must be about curl equations, not divergence equation.
I know what you mean. div E=\rho, curl E=0 <=> \nabla \nabla \phi=-\rho
However, which one is dependent in four electrostatics equations?
The Gauss law? or the one of curls?
And what are the algebraic structure of the four equations?
I think that the title of this thread is not good enough.
Maybe the following is better: How to explain the overdetermination of Electrostatic equations
4 equations and 3 unknowns
div E=\rho, curl E=0
everyone,
now we talk some simpler things, while not talking Maxwell equations.
Electrostatic fields equations
(1) \nabla \cdot E = \rho ,\nabla \times E = 0
There are four eqs, and three unknowns. How to explain it?
Here we only talk Eq. (1), while NOT talking the following...
In algebra, there are some vectors Yi (i=1,…,n) in a vector space. When there are coefficients (ci), not all zero, such that \sum\limits_{i = 1}^n {{c_i}{Y_i} = 0} ; The vectors Yi (i=1,…,n) are linearly dependent. Now I generalize the definition of linearly dependence in differential...
Maxwell's equations seem overdetermined, in that they involve six unknowns (the three components of E and B) but eight equations (one for each of the two Gauss's laws, three vector components each for Faraday's and Ampere's laws). (The currents and charges are not unknowns, being freely...
I know that BCS theory cannot explain high Tc superconductor.
Most high Tc superconductors belong to type-II ones.
Can BCS theory explain type-II conventional superconductor?
How to predict high Hc2 and low Hc1 for type-II conventional superconductor in BCS theory?
To Simon Bridge:
We both know no work can be done in a quasistatic isochoric process. However, a few (perhaps a lot of) persons generalize the result to all fixed volume processes including non-equilibrium processes.
An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant.
http://en.wikipedia.org/wiki/Isochoric_process
The isochoric...
the process is not quasi-static, the equation dw=pdV is not correct.
the high energy state relaxes to low energy state, the process usually is non-equilibrium. If the volume remains constant and it is no heat transfer, the difference of two energy states must do work to others.
My English is not good, but I think I can describe it clear.
The boxes in figure are rigid. There is a membrane with mass dividing the box into two parts. The left part is filled with high pressure gas, and the right part is filled with low pressure gas (or vacuum). The only difference between...
As we know photon's helicity are \pm1. Helicity is the projection of the spin S onto the direction of momentum, p, which is considered as Sz.
What about Sx and Sy? They are both ZERO?