What happens to a wire if only it's one end is connected to a terminal and if your answer is nothing then why nothing ? A battery should also produce an electric field outward as it does inside and free electrons in wire should get affected by it ! Please help !
If you connect a wire only to one terminal of a battery, the wire will be at the same potential as the terminal of the battery. If the other terminal of the battery is connected to ground, then your wire represents a capacitor with capacitance $C$ with respect to ground that will have a charge $Q=CV$, where V is the EMF of the battery.
For a very short time there will be a current in the wire. Charges will flow onto or away from the wire and free charges within the wire will also move, because of the electric field which you describe. After a short time the flow of charge (current) will stop. A new distribution of charge will be set up in the wire which opposes the electric field of the battery so that the resultant electric field in the wire is zero. Then no more charge flows in the wire in either direction.
There is not an electric circuit here, joining the +ve terminal of the battery to the -ve terminal, so the current does not keep flowing.