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.

 

[pmacias]

No, checking that ∇xE = 0 is not enough to verify that an electric field is possible in free space. In order for an electric field to exist in a given region of free space, there are several conditions that must be met. These conditions include the presence of charged particles, the absence of any external magnetic fields, and the absence of any conducting materials that could affect the distribution of charges. Additionally, the electric field must also satisfy Maxwell's equations, which include the condition that ∇xE = ρ/ε0, where ρ is the charge density and ε0 is the permittivity of free space. Therefore, simply checking that ∇xE = 0 is not enough to verify the existence of an electric field in free space. It is important to consider all of these conditions in order to accurately determine the possibility of an electric field in a given region.