I don't understand the notion "Electric field causes current in a conductor (metal wire)". Many textbooks say that free electrons in a metal wire are moved by elctric field (electrostatic?) - thus forming electric current.
If there is any electrostatic field outside a conductor, within that conductor that field is zero (= absent).
Current in a wire appears only when the circuit is "closed", but electrostatic field exists even if we have only one (say, only positive) charge (positive plug of a power battery), we do not need two charges-sources-of-field (positive and negative).
Positive plug of a power battery is a source of electrostatic field (it is charged positively - it is like a "point charge" creating electrostatic field). If we connect a metal rod to it (circuit is not closed) there would be no current in that rod, though we have electrostatic field (positive battery plug) and free electrons within the rod.
This "mysterious" electrostatic field that moves electrons in a closed-circuit wire is a composition (superposition) of two separate fields created by two "point-charges" - positive and negative plugs of a car battery. I have problems trying to visualize such a resultant field...
I put my metal rod exactly between positive and negative plugs of a car battery, but with a millimeter gap (rod not touching both plugs). There is almost same electrostatic field - same configuration=places in space of field-source-charges (positive and negative plugs), but there is no current. If the rod touches terminals however then there is current.
How was there eletric field in my rod without current?
How are there current in superconductors without eletric field?
This discussion adds to my confusion - in superconductor (ideal conductor) current exists without any electric (electrostatic?) field. And electric field causes current only in non-ideal conductors (not superconductors).
Interesting insight is given here, it attributes electrostatic field inside the conductor to surface charge gradient all along the metal wire.