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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?