Two infinite sheets of current flow parallel to the y-z plane as shown. The shee

Question

Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 5 cm. Each sheet consists of an infinite array of wires with a density n = 12 wires/cm. Each wire in the left sheet carries a current I1 = 3.1 A in the negative z-direction. Each wire in the right sheet carries a current I2 = 5.4 A in the positive z-direction.

4) What is integral B dot dL, where the integral is taken around the dotted path shown, from a to b to c to d to a. The path is a trapazoid with sides ab and cd having length 10.8 cm, side ad having length 5.5 cm, and side bc having length 10.4 cm. The height of the trapezoid is H = 10.5 cm.

6) What is integral B dot dL, where the integral is taken along the dotted line shown, from a to b?

Explanation / Answer

(4) Integral B.dL = u*I

I = current enclosed by the figure

u = 4*pi*(10^ -7)

I = current density*length

Current density for sheet 1 = current flowing/length

= 12*3.1/1 = 37.2 Amp/cm

I = 37.2*H = 37.2*10.5 = 390.6 Amp

Integral B.dL = 4*pi*(10^ -7)*390.6 = 4.908*(10^ -4)

(5)THE ABOVE INTEGRAL COMES FROM TWO PATHS c-d and a-b

because along c-b and d-a B.dL is zero .

So the B.dL is along c-d and a-b which is B*(dL along B) =B*H

hence B*H +B*H = u*I

2B*H = 4.904*(10^ -4)

B*H = 2.454*(10^ -4)

so line integral along path a-b is 2.454*(10^ -4)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.