3.Fundamentals of the Maxwell theory of the electromagnetic field. Displacement current. The Maxwell equation system in integral form and physical meaning of the equations.

The Maxwell theory of the electromagnetic field is a fundamental theory in physics that describes the behavior of electric and magnetic fields. It was developed by James Clerk Maxwell in the 19th century and is based on a set of four equations, known as Maxwell's equations.<br /><br />One of the key concepts in the Maxwell theory is the displacement current. The displacement current is a term that appears in Maxwell's equations and represents the rate of change of electric flux with respect to time. It is used to account for the effects of changing electric fields on magnetic fields.<br /><br />The Maxwell equation system in integral form is as follows:<br /><br />1. Gauss's law: The total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space.<br />2. Gauss's law for magnetism: There are no "magnetic charges" analogous to electric charges, and the magnetic field lines have no beginning or end.<br />3. Faraday's law of induction: The change in magnetic flux through a closed loop induces an electromotive force (EMF) in the loop.<br />4. Ampere's law with Maxwell's correction: The magnetic field around a closed loop is proportional to the electric current passing through the loop, with an additional term accounting for the displacement current.<br /><br />The physical meaning of these equations is as follows:<br /><br />1. Gauss's law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space. This equation is a statement of the conservation of charge.<br />2. Gauss's law for magnetism states that there are no "magnetic charges" analogous to electric charges, and the magnetic field lines have no beginning or end. This equation is a statement of the fact that magnetic fields are generated by the motion of electric charges.<br />3. Faraday's law of induction states that the change in magnetic flux through a closed loop induces an electromotive force (EMF) in the loop. This equation is a statement of the fact that changing magnetic fields can induce electric fields.<br />4. Ampere's law with Maxwell's correction states that the magnetic field around a closed loop is proportional to the electric current passing through the loop, with an additional term accounting for the displacement current. This equation is a statement of the fact that electric currents generate magnetic fields.