Electric charge motion, induced current, energy balance, and noise.

A general equation is derived which, through an arbitrary irrotational vector field, connects the electric charge carrier motion and the dielectric property of a system with its external currents, voltages, and powers. It is applied to generalize Ramo's theorem to any conducting medium and boundary condition, to compute the components of the energy balance, and to obtain a new, general, and straightforward relationship between carrier velocity and output noise which, to show its potentiality, is used here to evaluate the thermal noise.