 For a vector field on a compact manifold with a finite number of zeroes, the Poincaré-Hopf theorem states that the index of the vector field is equal to the Euler characteristic of the manifold.Michael Faraday, in his concept of "lines of force," emphasized that the field "itself" should be an object of study, which it has become throughout physics in the form of field theory.In addition to the magnetic field, other phenomena that were modeled by Faraday include the electrical field and light field.