Maxwell's equations. Vortex electric field. Bias current
Vortex electric field According to Maxwell's theory, any alternating magnetic field excites an electric field in the surrounding space, which is the cause of the induction current in the circuit - this is the first main position of Maxwell's theory. The circulation of the intensity vector E of this field along a closed loop L is large equal to the integral over a closed loop L from the projection of the intensity vector with indices b and l and is equal to the rate of change of the magnetic flux with a minus sign. By definition, the flow of the vector B is equal to the area integral S of the scalar product of the vector B, by the vector dS. The circulation of the intensity vector E of this field along a closed loop L is equal to the area integral S with a minus sign of the rate of change of the magnetic flux B. The electric field E with index b, excited by an alternating magnetic field, like the magnetic field itself, is vortex. The circulation of the total field E of this field along a closed loop L is equal to the area integral S with a minus sign of the rate of change of the magnetic flux B. The first equation of the Maxwell system of equations for the electromagnetic field. Displacement current Maxwell suggested that, similarly to a magnetic field, any change in the electric field causes a vortex magnetic field in the surrounding space. Maxwell called the alternating electric field the displacement current. In the field of a flat capacitor, the vector D is always directed from the positive plate to the negative one. But if the electric field increases, then the rate of change of the electric displacement D, and hence the displacement current, is directed as shown in the figure. If the electric field decreases, then the rate of change of the electric displacement D is directed from the negative plate to the positive one, and the magnetic field is opposite compared to the first case. The displacement current density is equal to the rate of change of the electric displacement D If there is an alternating current in any conductor, then an alternating electric field exists inside the conductor. Therefore, inside the conductor there is both a conduction current and a displacement current and the magnetic field of the conductor is determined by the sum of these two currents. The total current density J is equal to the sum of the conduction current J and the displacement current, which is equal to the rate of change of the electrical displacement D. Full current is always closed. Maxwell generalized the circulation theorem for the vector H by using the total current. The circulation of the vector H in a closed loop L is equal to the area integral S of the sum of the conduction current J and the rate of change of the electric displacement D. The generalized circulation theorem of the vector H is the second equation of the system of Maxwell equations for the electromagnetic field. Maxwell's equations in integral form Circulation of the total field E of this field in a closed loop L large is equal to the area integral S with a minus sign of the rate of change of the magnetic flux B Gauss's theorem for the field D: The flow of the vector D through the surface S is equal to the volume integral of the volumetric charge density. The circulation of the vector H in a closed loop L is equal to the area integral S of the sum of the conduction current J and the rate of change of the electrical displacement D Gaussian theorem for the field B: The flux of the vector D through the surface S is equal to zero. The system of material relations In order for this system of equations to be complete , it must be supplemented with material relations. The electric displacement vector D is equal to the product of the electric constant and the electric permeability of the medium and the vector of the electric field intensity E The magnetic induction vector B is equal to the product of the magnetic constant mu, zero, to the magnetic permeability mu and to the magnetic field strength H The conduction current J is equal to the product of the specific conductivity of the Gamma substance and the electric field strength.
Maxwell's equations in differential form The rotor of the intensity vector E is equal to the rate of change of magnetic induction with a minus sign The divergence of the electric displacement vector D is equal to the volume charge density rho The rotor of the magnetic field H is equal to the sum of the currents: the conduction current J and the displacement current, which is equal to the rate of change of the electrical displacement D The divergence of the magnetic induction vector B is equal to zero.