Magnetic Fields from Two Infinite Sheets of Current 1 2 3 4 5 6 7 Two infinite s

Question

Magnetic Fields from Two Infinite Sheets of Current

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Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 5.5 cm. Each sheet consists of an infinite array of wires with a density n = 14 wires/cm. Each wire in the left sheet carries a current I1 = 3.2 A in the negative z-direction. Each wire in the right sheet carries a current I2= 3.1 A in the positive z-direction.

1)

What is Bx(P), the x-component of the magnetic field at point P, located at (x,y) = (-2.75 cm, 0)?

T

2)

What is By(P), the y-component of the magnetic field at point P, located at (x,y) = (-2.75 cm, 0)?

T

3)

What is By(R), the y-component of the magnetic field at point R, located at (x,y) = (-8.25 cm, 0)?

T

4)

What is

B dl Bdl

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 11 cm, side ad having length 6 cm, and side bc having length 8.4 cm. The height of the trapezoid is H = 10.9 cm.

T-m

5)

What is By(S), the y-component of the magnetic field at point S, located at (x,y) = ( 8.25 cm, 0)?

T

6)

What is

abB dl abBdl

where the integral is taken along the dotted line shown, from a to b.

T-m

Explanation / Answer

1) Bx = 0

2) B = uo*n*Itot/2 = (4pi*10^-7*1400*6.3)/2 = 5.54*10^-3 T (-y-direction downward)

3) By(R) = (4pi*10^-7*1400*-0.1)/2 = 8.8*10^-5 T (+y-direction upward)

4) B.dl = u*Ienclosed = u*I*n*H = (4pi*10^-7*3.2*1400*0.109) = -6.14*10^-4 (minus sign is due to against the direction of magnetic field)

5) By(S) = 8.8*10^-5 T (-y-direction downward)

6) B.dl = BP*H = 5.54*10^-3*0.109 = 6.04*10^-4

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