What makes electric field zero in a wire? Take a ideal inductor (superconductor). Change in magnetic field produces electric field. But in a ideal inductor electric field inside is zero.
What makes the electric field zero in a ideal inductor when it
is connected to a circuit.
Another question is why is electric field inside a ideal conducting wire zero when it is connected in a circuit.
 A: In the steady state condition, there is no electric field inside a perfect conductor because the electrons have moved to cancel out any electric field.  That is because electrons will move whenever there is an electric field.
However, while the electric field inside a conductor is changing, there is a lag between the imposition of the new field and the rearrangement of the electrons.  Primarily this is due to inductance.  As a result, there is an electric field inside a conductor while the imposed electric field is changing and, in the case where the imposed field is changed in a single abrupt step, during the brief time while the electron distribution is changing to its new steady-state condition.
A: Resistance, R, is defined as voltage drop/current.  If R is zero, then the voltage drop and the E field must be zero. Zero resistance does not imply that the current is infinite.  If a superconductor is part of a circuit with other elements which do have resistance, then the other elements determine the current. (Consider a superconducting long distance power line.) In most applications the superconductor is the circuit (such as a large electromagnet.) Then the problem becomes: How do you introduce a current? (Always a limited process).
