Clerk Maxwell's paper A Dynamical Theory of the Electromagnetic Field. Maxwell used calculus to exhibit Michael Faraday's theory, that light is an electromagnetic phenomenon. Maxwell introduced the term D, specific capacity of electric induction, in a form different from the modern and familiar notations. It was Oliver Heaviside who reformulated the complicated Maxwell's equations to the modern form. It wasn't until 1884 that Heaviside, concurrently with Willard Gibbs and Heinrich Hertz, grouped the equations together into a distinct set. This group of four equations was known variously as the Hertz–Heaviside equations and the Maxwell–Hertz equations, and is sometimes still known as the Maxwell–Heaviside equations; hence, it was probably Heaviside who lent D the present significance it now has. Example: Displacement field in a capacitor Consider an infinite parallel plate capacitor where the space between the plates is empty or contains a neutral, insulating medium. In this case there are no free charges present except on the metal capacitor plates. Since the flux lines D end on free charges, and there are the same number of uniformly distributed charges of opposite sign on both plates, then the flux lines must all simply traverse the capacitor from one side to the other, and outside the capacitor. In SI units, the charge density on the plates is equal to the value of the D field between the plates. This follows directly from Gauss's law, by integrating over a small rectangular box straddling one plate of the capacitor: On the sides of the box, dA is perpendicular to the field, so the integral over this section is zero, as is the integral on the face that is outside the capacitor where D is zero. The only surface that contributes to the integral is therefore the surface of the box inside the capacitor, and hence where A is the surface area of the top face of the box and is the free surface charge density on the positive plate. If the space between the capacitor plates is filled with a linear homogeneous isotropic dielectric with permittivity , then there is a polarization induced in the medium, and so the voltage difference between the plates is where d is their separation. Introducing the dielectric increases ε by a factor and either the voltage difference between the plates will be smaller by this factor, or the charge must be higher. The partial cancellation of fields in the