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Consider the above question. I have been able to solve the question understanding area vector of A and B are opposite in direction.

However I have some conceptual doubts.

  1. In Faraday Law, when we say "area enclosed by a closed loop", does it coherently include all type of loops -- with twists and turns as given in the above question.

  2. Suppose I take only one loop say A and I try to apply Faraday in it. Can I do so simply while ignoring B?

Tony Stark
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1 Answers1

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  1. Yes, the loops in question can be quite exotic. As long as the loop does not intersect itself, you can find an oriented surface which has that loop as its boundary$^\dagger$. The integral form of Faraday's law (which obtained from the differential form by application of Stokes' Theorem) can then be applied from there.
  2. Yes, you can get away with that here. Strictly speaking, we should only consider non-intersecting loops. However, if we allow a finite number of intersections and then decompose the result into a "sum" of non-intersecting loops, then we will get the same result when we add things back together. Of course, we'll have to pay attention to the orientations of each piece.

$^\dagger$The general procedure for constructing such a surface is called the Seifert algorithm.

Albatross
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