The figure shows, in cross section, several conductors that carry currents throu

Question

The figure shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes I1 = 3.8 A , I2 = 6.4 A , and I3 = 1.9 A , and the directions shown. Four paths, labeled a through d, are shown. (Figure 1)

A) What is the line integral ?B? ?dl? for the path b? The integral involves going around the path in the counterclockwise direction.

B)What is the line integral ?B? ?dl? for the path c? The integral involves going around the path in the counterclockwise direction.

C)What is the line integral ?B? ?dl? for the path d? The integral involves going around the path in the counterclockwise direction.

Explanation / Answer

According to Ampere's law

interal B.dl = mue*I_enclosed

a) integral B.dl = mue*(-I1)

= -4*pi*10^-7*3.8

= -4.78*10^-6 T.m

b) integral B.dl = mue*(I2 -I1)

= 4*pi*10^-7*(6.4 - 3.8)

= 3.27*10^-6 T.m

c) integral B.dl = mue*(I2 + I3 -I1)

= 4*pi*10^-7*(6.4 + 1.9 - 3.8)

= 5.65*10^-6 T.m

here current coming out of the page is positive

and current going in to the page is negative.

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