Question

The figure shows two closed paths wrapped around two conducting loops carrying currents i1 = 8.1 A and i2 = 4.5 A. What is the value of the integral Bds for (a) path 1 and (b) path 2?

The figure shows two side-by-side rectangles that each represent a conducting loop. On top of the loop on the left, an arrow pointing right is labeled i subscript 1. On top of the loop on the right, an arrow pointing right is labeled i subscript 2. Two closed paths labeled 1 and 2 wrap around the vertical sides of the conducting loops. ● Path 1 is circular and wraps around the top inner sides of the loops. It is in the counterclockwise direction. ● Path 2 wraps around the bottom of three sides and crosses itself at two points. ○ Starting arbitrarily from the front of the left side of the left loop, Path 2 goes left and then around to the back of that same left side and comes out the center of the left loop. ○ It comes around to the front of the right side of the left loop. ○ It goes around the back of the left side of the right loop. ○ It then goes around to the front of that same left side. ○ It crosses itself and goes around the back of the right side of the left loop. ○ It then crosses itself in the middle of the left loop and starts over again.

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Answer #1

Path 1: (Beds & Mo (-8.1 +4.5) = 47x60-7(-8.1+4.5) Bods = – 4.52x106 path 2 : Seuds = 471x10 + (-8.1-8.1 -4.5) Bods = – 2.60x

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