This should be simple but I know I'm going wrong somewhere and I can't figure out where. The curl of a electric field is zero, i.e. [itex]\vec { \nabla } \times \vec { E } = 0[/itex] Because , no set of charge, regardless of their size and position could ever produce a field whose curl is not zero. But, Maxwell's 3rd Equation tells us that, the curl of a electric field is equal to the negative partial time derivative of magnetic field [itex] \vec {B}[/itex]. i.e. [itex]\vec { \nabla } \times \vec { E } = -\frac { \partial }{ \partial t } \vec { B } [/itex] So is the curl zero or is it not? If we equate those two equations we get that the time derivative of magnetic field is zero. What's wrong? What am I missing?
That should read, "the curl of an electrostatic field is zero," that is, the electric field associated with a set of stationary charges has a curl of zero. In this situation, there is no magnetic field, so ##\partial \vec B / \partial t = 0##.