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A vector analysis of a group of equations often called the Maxwell equations is given. Actually Maxwell's feather belongs to one equation, in which he introduced the so-called "bias current". The analysis shows that this current is a superfluous addition and prevents mutual consistency of the equations of the group.After excluding this current, the wave properties of the electric and magnetic fields disappear. Electric and magnetic fields cease to be "special form of matter".Further, a summary of the foundations of new electrodynamics without Maxwell's equation is given, and a group of equations with no internal contradictions is recorded. The Coulomb law and the laws of interaction of currents and equations of potentials are taken as a basis. The law of electromagnetic induction is formulated in a new way.The beginning of a new theory of radio wave propagation is given. The last part gives examples of detailed, complete calculation of electrical and magnetic potentials of typical sources. The book is intended for researchers, teachers, postgraduates, teachers and students.