The electric field depends on the potential difference (voltage) between the wires in the cable, not on the current going through the wires. The electric field will be strongest inside the cable, between the 'live' wire and the 'neutral', and between the live wire and the 'Earth' wire, but the field will also be present outside the cable, forming the well-known field pattern of an electric dipole.
If a current does flow through the wires in the cable (because the device at the end of the cable is turned 'on') there will also be a weak alternating magnetic field in and around the cable. The field will be weak because the cable carries equal currents in opposite directions, but not zero, because the currents are separated by a small distance.