Are there Electrostatic Fields at infinity?

[cmd2002]

Homework Statement

In the region x ≥ 0 there is an electrostatic potential V(x)=xexp(-λx) where λ>0
What is the electrostatic field at x→∞

Homework Equations

The Attempt at a Solution

My understanding is there is no fields at infinity because there is no electrostatic potential?
Sorry but I am so confused?

 

[vela]

How are the electric field E and the potential V related?

 

[cmd2002]

I believe Potential energy is the energy off one charge in relation to another charge. Therefore creating electrostatic fields? help:(