Exercise 28.40 Part A The figure shows, in cross section, several conductors tha

Question

Exercise 28.40 Part A The figure shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes 11-3.6 A , 12-6.4 A , and I3 2.1 A, and the directions shown. Four paths labeled a through d, are shown. (Figure 1) What is the line integral B dl for the path a? The integral involves going around the path irn the counterclockwise direction. Express your answer using two significant figures. Submit My Answers Give Up Part B What is the line integral B dl for the path b? The integral involves going around the path irn the counterclockwise direction. Express your answer using two significant figures. Figure 1 of 1 Submit My Answers Give Up Part C What is the line integral B dl for the path c? The integral involves going around the path irn the counterclockwise direction. 3 Express your answer using two significant figures. Submit My Answers Give Up

Explanation / Answer

part A:

from Ampere law closed integral of B.dL = uo I

so for path A,

Curent Enclosed is 0,

so B.dL = 0

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for pathB,

I1 = = 3.6 A

so

B.dL = 4pi e-7 * 3.6

B.dL = 4.52 *10^-6 Tm
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for path C, Current I = I1 - I2

I = 3.6 - 6.4 = 2.8 A

so B.dL = uo * 2.8

B.dL = 4pi e-7 * 2.8 = 3.51 *10^-6 T m

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for path D:

Inet = I1 - (i2+i3)

Inet = 3.6 -(6.4 + 2.1)

Inet = 4.9 Amps

so

B.dL = 4pie -7 * 4.9

B.dL = 6.15 *10^-6 Tm

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