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

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      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)

In (1.117), is defined as the phasor form of the function g(r,t) and expressed as

      (1.118)

      This can be applied for vectorial function as

      (1.119)

      The representation of the time harmonic functions in phasor form provides several advantages. They convert the time domain differential equations to frequency domain algebraic equations. This can be better understood by studying the derivative property as follows. Let's take derivative function g(r,t) with respect to time as

(1.120)

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