How does the battery create an electric field inside the conducting wire connected to its terminal?

Question

In books, it is not explained exactly how the battery creates an electric field inside the wire. Also, is that the electric field inside the wire only or is it present outside the wire as well?

Answer 1

If the two ends of a length of uniform wire are connected to the terminals of a battery, the battery will pull electrons from one end of the wire and place them on the other end. The total charge on the wire will be zero, but one end will have a positive charge/unit length and the other end will be negative. The system quickly reaches equilibrium with a continuous flow of current, driven by a uniform electric field in the wire which is proportional to the gradient of the charge density. For the potential difference between the two ends of the wire to be independent of the radius, the parallel component of the field in the wire must also be independent of the radius. Any symmetrical radial component would tend to push charges outward. This suggests that the excess charge in any segment of the wire will be found at the surface, but the magnetic field produced by the current may work against this effect. For Gauss's law to be true for any chosen segment of the wire, field lines must be leaving the sides of the positive half of the wire and reentering along the negative half.

Answer 2

if there is no wire you have an electric field between the poles of the batterie. If you connect the poles with a wire, a current will flow, driven by the electric field and the electric field is only inside the wire, outside you will have a magnetic field around the wire.

Answer 3

In books, it is not explained exactly how does the battery creates electric field inside the wire.

A @trula explained, the battery creates an electric field between its terminals. But with nothing connected between the terminals (infinite impedance) this field cannot produce a current. A wire with a resistance $R$ connected between the terminals allows a current $I$ to flow where $I=V/R$ where $V$ is the battery voltage across the terminals when delivering current $I$.

Also, is that the electric field inside the wire only or is it present outside the wire as well?

This question has already been asked here: Does a current carrying wire produce electric field outside?

The reference cited in the accepted answer says there is an electric field outside the wire.

Hope this helps.