Item 8 The figure shows, in cross section. several conductors that carry current

Question

Item 8 The figure shows, in cross section. several conductors that carry currents through the plane of the figure. The currents have the magnitudes I1 = 4.5 A, I2 = 5.9 A, and I3 = 1.9 A. and the directions shown. Four paths, labeled a through d, are shown. (Figure 1) Express your answer using two significant figures. Part A What is the line integral close int B . dl for the path a? The integral involves going around the path in the counterclockwise direction. Part B What is the line integral close B . dl for the path b? The integral involves going around the path in the counterclockwise direction. Express your answer using two significant figures. Item 8 Part C What is the line integral close int B. dl for the path C? The integral involves going around the path in the counterclockwise direction. Part D Express your answer using two significant figures. What is the line integral close int B . dl for the path d? The integral involves going around the path in the counterclockwise direction.

Explanation / Answer

a)

path a : no current is inside that path , thus line integral equals 0 Tm

b)

path b :

= u0 * I1 = 4 * 3.14 * 10^-7 * 4.5 = 5.6 * 10^-6 Tm

c)

for path c:

= u0 * (I2 - I1) = 4 * 3.14 * 10^-7 * (5.9 - 4.5 ) = 1.75 * 10^-6 Tm

d)

for path d:

= u0 * ( -I1 + I2 + I3)

= 4 * 10^-7 * 3.14 * ( -4.5 + 5.9 + 1.9 ) = 4.1 * 10^-6 Tm

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