Three long, parallel conductors carry currents of I = 1.58 A. The figure below i

Question

Three long, parallel conductors carry currents of I = 1.58 A. The figure below is an end view of the conductors, with each current coming out of the page. Taking a = 1.50 cm, determine the magnitude and direction of the magnetic field at points A, B, and C.

BA : Magnitude______ µT Direction: to the left, to the right, upward, downward, into the page, out of the page, or none BB : Magnitude______ µT DirectionL to the left, to the right, upward, downward, into the page, out of the page, or none BC : Magnitude _____ µT Direction: to the left, to the right, upward, downward, into the page, out of the page, or none

Explanation / Answer

AT A
Distance from wires to A = sqrt (a^2 + a^2) = sqrt (2 a^2) = sqrt (2 x (.015)^2) = 0.02121 m

B1 = mo I / 2 pi d = (4 x pi x 10^-7 x 1.58) / (2 x pi x .02121) = 14 micro T

B2 = mo I / 2 pi d = (4 x pi x 10^-7 x 1.58) / (2 x pi x .02121) = 14 micro T

B3 = mo I / 2 pi 3a = (4 x pi x 10^-7 x 1.58) / (2 x pi x .015 x 3) = 7.02 micro T

B1 and B2 are perpendicular and of equal magnitude so B" = B x sqrt(2) = 14 x sqrt (2) = 19.79 microT   

Bnet = BA = B" + B3 = 19.79 + 7.02 = 26.81 microT (downwards)

AT B
Bnet due to both above and lower wire = 0 (because of equal magnitude and opposite direction)

B 3 = BB = mo I / 2 pi 2a = (4 x pi x 10^-7 x 1.58) / (2 x pi x 2 x .015) = 10 micro T (downwards)

AT C
B1 = mo I / 2 pi d = (4 x pi x 10^-7 x 1.58) / (2 x pi x .02121) = 14 micro T

B2 = mo I / 2 pi d = (4 x pi x 10^-7 x 1.58) / (2 x pi x .02121) = 14 micro T

B3 = mo I / 2 pi a = (4 x pi x 10^-7 x 1.58) / (2 x pi x .015) = 21 microT

B1 and B2 are perpendicular and of equal magnitude so B" = B x sqrt(2) = 14 x sqrt (2) = 19.79 microT (upward)

Bnet = BC = B3 - B" = 21 - 19.79 = 1.21 microT (upward)

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