Conditions for a E field to be possible

[cutesteph]

If I want to verify an electric field E is possible in free space, do I just need to check ∇xE =0?

 

[WannabeNewton]

In free space what always has to hold is $\vec{\nabla}\cdot \vec{E} = 0$ whereas $\vec{\nabla}\times \vec{E} = 0$ only holds in electrostatic systems. Is your system electrostatic?

 

[cutesteph]

Yes, the system is electrostatic.

 

[WannabeNewton]

Then yes you have to check that the electric field is irrotational. You also have to check that it is divergence-free.