5. A wire of circular cross section carries a current I. In Figure 2 an Amperian

Question

5. A wire of circular cross section carries a current I. In Figure 2 an Amperian loop in the shape of a hexagon is surrounding the wire. The plane of the hexagon is perpendicular to the wire. The length of each side of the hexagon is 5.0 cm. The magnitude and direction of the magnetic field (due to ID at the center of each shown side of the hexagon is given. 32 (10°) Approximate the line integral fBdS by calculating , L. , a. . 25pT 2.5 HT (20°) where L is the length vector of the ith side. (The acute angle each vector B, makes with L, is shown in parentheses.) 3.2 T 2.1 HT Use Ampere's law to estimate I. What is the direction of this current? 29uT C (12) (15°) b. Figure 2

Explanation / Answer

given the magnitude and direction of magnetic field at the center of each side of the amperean loop

a. now, B.ds has to be calculated for each side

so for the zix sides given

dl = 0.05 m

B.dl = (3.2 + 3.2 + 2.9cos(15) + 2.1cos(12) + 2.5cos(20) + 3cos(10))*10^-6*0.05

B.dl = 0.82794*10^-6 Tm

b. now from ampere's law

B.dl = mu*i

hence

0.82794*10^-6 = 4*pi*10^-7*i

i = 0.658859 A

the dfirecxtion of the curent is out of the plane of the page

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