It is tempting to generalize Faraday's law to state: "If ' is any arbitrary closed loop in space whatsoever, then the total time derivative of magnetic flux through ' equals the EMF around ""." This statement, however, is not always true and the reason is not just from the obvious reason that EMF is undefined in empty space when no conductor is present. As noted in the previous section, Faraday's law is not guaranteed to work unless the velocity of the abstract curve matches the actual velocity of the material conducting the electricity. The two examples illustrated below show that one often obtains incorrect results when the motion of is divorced from the motion of the material.