Electric fields

[uzair_ha91]

When a DC flows through a wire, does the electric field vary?
If a changing electric flux produces a magnetic field, then electric field will have to vary constantly, right?
If that's not the case, then what produces a magnetic field around a conductor carrying current?

[user111_23]

When a DC flows through a wire, does the electric field vary?
If a changing electric flux produces a magnetic field, then electric field will have to vary constantly, right?
If that's not the case, then what produces a magnetic field around a conductor carrying current?

Yes, that is correct.

The motion of the electrons is what causes the magnetic field to appear.