## Interpretations of Maxwells Equations

Maxwell's equations may be presented in words as follows:

I The electric flux (surface integral of the electric flux) through a closed surface is equal to the total charge within the volume confined by the surface.

II The magnetic flux (surface integral of the magnetic flux) through any closed surface is zero.

III The line integral of the electric field along a closed contour is equal to the negative time derivative of the magnetic flux through the closed contour.

IV The line integral of the magnetic field along a closed contour is equal to the sum of the total current through the closed contour and the time derivative of the electric flux.

Figure 2.1 illustrates Maxwell's equations in integral form. These qualitative interpretations are as follows:

I The distribution of the electric charge determines the electric field.

II The magnetic flux lines are closed; in other words, there are no magnetic charges.

III A changing magnetic flux creates an electric field.

IV Both a moving charge (current) and a changing electric flux create a magnetic field.

The creation of an electromagnetic field is easy to understand qualitatively with the aid of Maxwell's equations. Let us consider a current loop with a changing current. The changing current creates a changing magnetic field (IV); the changing magnetic field creates a changing electric field (III); the changing electric field creates a changing magnetic field (IV); and so on. Figure 2.2 illustrates the creation of a propagating wave.

Maxwell's equations form the basis of radio engineering and, in fact, of the whole of electrical engineering. These equations cannot be derived from other laws; they are based on empirical research. Their validity comes from their capability to predict the electromagnetic phenomena correctly. Many books deal with fundamentals of the electromagnetic fields, such as those listed in [1—8].

Figure 2.2 Electromagnetic wave produced by a current loop.

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