Ampere's law, modified form:

The line integral of the magnetic field about a closed curve is proportional to the total of two terms: first one, the algebraic total of electric currents passing through that closed curve; and second one, the instant time rate of change of the electric flux by a surface limited by that closed curve; in differential form,

curl H = J + dD/dt,

where d/dt revel partial differentiation.

Additionally to defining electromagnetism, his equations also predict which waves can propagate by the electromagnetic field, and always would propagate at the similar speed these are electromagnetic waves; the speed can be determined by calculating (epsilon₀ mu₀)^-1/2, which is c, the speed of light within vacuum.