# 16 Examples of Faraday's Law - Lecture 18 Examples of...

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Lecture 18 Examples of Faraday’s Law. So far we have seen that magnetic circuits can be either linear or nonlinear. They can also be fixed or have moving parts. Both can be characterized by an inductance matrix L, which in the latter case will be dependant of the variable x (position). It is in general difficult to obtain matrix L by inspection and therefore easier to do it systematically by solving the magnetic circuit. Example 1 . Consider the following non-moving magnetic circuit. This has the following equivalent circuit, Φ 1 = Φ 2 . Then by loop analysis, () 11 2 2 1 1 2 1 3 33 3 3 2 3 1 Ni += Φ + Φ Φ =ℜΦ +ℜ Φ −Φ By simple algebraic manipulation and substitution one can find that,

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() 11 2 3 2 2 3 3 2 1 21 2 3 2 2 3 3 2 2 12 13 23 31 2 2 2 3 1 2 3 1 N NN i N i N i Φℜ + +   Φ= Φ = ℜ +ℜ ℜℜ +ℜℜ +ℜℜ +  And since NL i λ = then diag N Li = , therefore 2 3 1 22 3 1 3 2 2 2 3 2 2 3 232 2 132 3 1 2 1 N N N LN N
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16 Examples of Faraday's Law - Lecture 18 Examples of...

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