ТОП просматриваемых книг сайта:
Introduction To Modern Planar Transmission Lines. Anand K. Verma
Читать онлайн.Название Introduction To Modern Planar Transmission Lines
Год выпуска 0
isbn 9781119632474
Автор произведения Anand K. Verma
Издательство John Wiley & Sons Limited
It is observed that in the absence of the external sources, in a lossless medium Maxwell’s equation (4.4.1a) states that a time‐varying magnetic field creates a time‐varying electric field; and Maxwell’s equation (4.4.1b) states that a time‐varying electric field (
Equation (4.4.1c) of Maxwell's equations is a divergence relation. It shows that the electric field originates from a charge, and ends on another charge. Equation (4.4.1d) shows that the divergence of the magnetic field is zero; meaning thereby that a magnetic charge does not exist in nature. The magnetic field exists as a closed‐loop around a current‐carrying conductor. However, sometimes a presence of the hypothetical magnetic charge is assumed, and the divergence equation (4.4.1d) is modified as
(4.4.4)
Figure 4.8 Surfaces and volume used in the integral form of Maxwell equations.
In a real material medium, a current can flow due to the time‐dependent electric polarization (P), and also due to the time‐dependent magnetic polarization (M). These are known as the electric and magnetic polarization currents and are incorporated in Maxwell’s equations as the electric and magnetic displacement current densities. Sometimes, the external sources, magnetic current density
A divergence of Maxwell’s equations (4.4.1b) in absence of
(4.4.5)
The above equation shows the conservation of charge. In any enclosed volume, the decrease of charge is associated with a flow of current out of the volume.
Normally, the time‐harmonic fields are used in most of the applications. The time‐dependent electric field and other field quantities are written in the phasor form for the time‐harmonic field:
(4.4.6)
(4.4.7)
It is noted that the same notation is used for both the time‐space dependent fields [
(4.4.8)
Using the above equation for the electric field and similar equation for the magnetic field, Maxwell’s equations (4.4.1), in the external source free medium, are rewritten below in the phasor form for the time‐harmonic field: