Difference btw induced and static electric field.

[lavesh]

∇x E≠0 for an induced electric field whereas for field produced by static charges we have ∇x E=0.
This is a very huge difference in the property of a vector field,then why do we call both of them electric field ?

 

[jtbell]

They both exert forces on charges according to ${\vec F}_e = q \vec E$.

Also, in relativity we don't distinguish between the two kinds of electric field when transforming from one reference frame to another via the Lorentz transformation. In the electromagnetic field tensor, it's always the sum of the two (i.e. the total electric field) that appears.

http://en.wikipedia.org/wiki/Electromagnetic_tensor

 

[HomogenousCow]

you could call them different things, but they exert forces the same way so it's convenient to just add them up.