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Question 1: demonstration

The average value of the potential Pj is equal to (figure 3)

Figure 3

Between and the potential we have the relation:

respectively

And therefore we have

The development in Fourier series of the potential Pj only includes cosine terms because of the wave form's symmetry in relation to .

The first harmonic of Pj (the term in ) has the amplitude (figure 4).

Either

As

we finally have

The second harmonic of PA (the term in ) has the amplitude

Either

As

we finally have

 

And so forth.

Figure 4

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Last update: 2005, September, 30 | Translation: Sergiu Ivanov