Hi. I am trying to understand Maxwell's equations. I am used to Gaussian units. The following sums up what I do not understand. (Or at least one thing I do not understand ... ) Let x0 be a position situated in a vacuum, with no photons in it, next to an infinite pane of glass. Ions arrive at the glass on the other side. What happens to the electric field at x0? Due to the Coulombic potential from the arriving ions, common sense tells us that the electrostatic potential gradient at x0 is changing, and that an electric field is therefore increasing in magnitude. However, Faraday's equation (microscopic, differential) reads dB/dt = -c ∇× E Since there is no current at x, the Ampere-Maxwell equation reads dE/dt = c ∇× B If both the electric and magnetic fields are regarded as locally determined, this means that the information about the E field has to propagate from the glass to x0 as a wave involving the B field. But we said the glass was infinite, say in the y and z direction, so dE/dt at the glass (caused by the current of ions arriving) could be constant in y and z. Then everywhere, ∇×E is zero (Ex is constant in y and z, Ey=Ez=0) so B should not be changing anywhere. It seems like under Maxwell, the location x0 will never experience the electric field from the nearby charge accumulation. What did I do wrong? To put it another way, are there situations where applying Maxwell's equations - or at least, the differential version of them - is not physically correct? The reason I ask this is that I am working on a problem involving a quasineutral plasma filament in a DC circuit. My real paradox is different: Ampere's equation J = c/4π ∇× B approximately holds, and it then follows from Faraday, and Gauss (Div E = 0) that dJ/dt = c2/4π ∇2 E. However, for Coulomb gauge magnetic potential A, it also follows from Ampere that J = -c/4π ∇2 A, so it follows (by equating expressions for dJ/dt) that ∇2 E = -1/c ∇2 dA/dt from which it follows that the electrostatic gradient satisfies Laplace's equation. But therefore from dJ/dt = c2/4π ∇2 E, the p.d. has no influence on the current flowing! I'm not a physicist so it's not surprising that I got confused, but it's very important that I get to grips with this problem. Any help much appreciated.