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The name given by J. C. Maxwell to the term ∂ D /∂t which must be added to the current density i to extend to time-varying fields the magnetostatic result of A. M. Ampère that i equals the curl of the magnetic intensity H . In integral form this result is given by the equation below,
If one defines current as a transport of charge, the term displacement current is certainly a misnomer when applied to a vacuum where no charges exist. If, however, current is defined in terms of the magnetic fields it produces, the expression is legitimate.
In establishing the theory of the electromagnetic field, J. C. Maxwell proposed a hypothesis— later confirmed by experiment—stating that a magnetic field is created not only by the motion of charges (conduction current, or simply current) but also by any change in the electric field over time. Maxwell designated as “displacement current” a quantity equal to the change over time t of the induction D—or, more accurately, the quantity (∂D/∂t)/4π. The rotational magnetic field is determined by the total current j = jcond + (∂D/∂t)/4π, where jcond is the conduction current density. A displacement current creates a magnetic field according to the same law that applies to a conduction current; it is for this reason that the designation “current” is applied to the quantity (∂D/∂t)/4π. (SeeMAXWELL’S EQUATIONS.)