# Does a Changing Electric Field Between The Plates of a Charging Capacitor Really Create a Magnetic Field?

Maxwell asserted that a virtual current. the displacement current, which was proportional to the charging field between the plates was sufficient to produce a magnetic field of the same orientation as the magnetic field surrounding the charging conductors connected to the capacitor plates. The fact that no charging electrons needed to be present was the basis of his theory of electromagnetism since a changing electric field alone could produce a magnetic field.

Do the mobile electrons in the connecting wires lose their ability to generate a magnetic field when they flow onto the capacitor plates? The left hand rule for negative charge gives the field above the charging wire as entering into the x y plane and its return exiting below that conductor, and is consistent with the circular field surrounding the wire. When electrons flow onto the upper plate the same rule gives the field on the left of the plate to be entering the xy plane and its return exiting on the right side of the plate.

When the electron current flows onto the bottom plate the rule gives the magnetic field as exiting the x y plane on the left side of the plate but entering the x y plane on the right of the plate.

For every electron that arrives on the left plate another electron leaves the right plate, driven by the attraction of the battery and the Coulomb repulsion of the left plate. For the electrons leaving the top right plate the rule gives the direction of the magnetic field produced on the left side of the top right plate as exiting on the left side and entering on the right side of the plate which means that between the top plates the field is exiting. The rule then gives the field as entering the x y plane between the bottom plates. Thus there is a magnetic field between the plates which is opposite in circulation to the fields surrounding the charging wires.

This contradicts the displacement current notion that the magnetic field between the plates has the same direction of circulation as that of the charging wires and is solely a consequence of the changing electric field.