RF/Microwave Engineering and Applications in Energy Systems. Abdullah Eroglu

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From (1.103) and (1.105), we can now write as

(1.105)

      or

(1.106)

In (1.106) i_s is the current through the surface S. Equation (1.106) is the integral form of the equation given in (1.89).

Similarly, we can express the integral form of Eq. (1.88) as

      (1.107)

      As a note, it is assumed that the magnetic current source does not exist. Taking the volume integral of both sides over volume V and surface S gives

(1.108)

We now apply divergence theorem as described in Section 1.3.5 for the left‐hand side of the equation in (1.108) as

(1.109)

From (1.108) and (1.109), we can write

(1.110)

Equation (1.110) is the integral form of the equation given in (1.91). Similarly, the integral form of Eq. (1.90) can be found as

      (1.111)

      In summary, the integral forms of Maxwell's equations are

      (1.112)

      (1.113)

      (1.114)

      (1.115)

1.5 Time Harmonic Fields

      Let's assume we have a sinusoidal function that changes in position and time. This function can be expressed as

(1.116)

Equation (1.116) can rewritten as

(1.117)СКАЧАТЬ