- The conductor as a whole is neutral so why would it produce a magnetic field?(I mean there aren't any net charges moving around)
In a neutral current-carrying wire, the charges are balanced. This means that the wire does not produce an electric field. However, a magnetic field is still induced due to the presence of flow of charges.
A magnetic field is produced only when a charged particle is moved. Let us first consider a charged particle, say, an electron in its rest frame. It would only be noticed to produce and electric field, and no magnetic field at all. However, should we change our reference frame to something that is moving with relative velocity to this electron, say another electron, it would not only be observed to be accelerating, but undergoing rotation (a form of acceleration)!
Now to account for the rotation, it is posited that in the second frame of reference from another electron, there is a magnetic field, in addition to the electric field, that rotates the charge.
Having no net charges moving around simply means that there is no electric field.
- If we take a neutral wire and begin to move it (physically, no current in the wire), will it still produce a magnetic field?(I know it sounds silly but I want to know why this idea doesn't work?)
There is a difference between a neutral wire and a wire with no current. Look back at the definition of current, defined as the flow of electric charge. In this case, there is no potential difference, hence no flow of electric charge. Hence, moving a wire with no current is impossible to produce an electric field nor a magnetic field.