The drawing shows an end-view of three wires. They are long, straight, and perpe

Question

The drawing shows an end-view of three wires. They are long, straight, and perpendicular to the plane of the paper. Their cross sections lie at the corners of an isosceles triangle (a = 10.0 m, b = 5.50 m). The current ( I 1 ) is going out of the page and it is equal to 13.5 A, the current ( I 2 ) is going into the page and it is equal to 8.00 A, and the current ( I 3 ) is going out of the page and it is equal to 9.00 A. What is the magnitude of the magnetic field at point (P), which is located half way between wire (2) and wire (3)? (T)

Explanation / Answer

magnetic field due to wire 1 , B1x = uo*I1/(2*pi*r1)

r1 = sqrt(a^2+(b/2)^2) = sqrt(10^2+2.75^2) = 10.4 m

B1 = 4*pi*10^-7*13.5/(2*pi*10.4) = 2.6*10^-7 T

r2 = r3 = b/2

magnetic field due to wire 2 , B2y = -uo*I2/(2*pi*r2)

B2y = -4*pi*10^-7*8/(2*pi*2.75) = -5.82*10^-7 T

magnetic field due to wire 3 , B3y = -uo*I3/(2*pi*r3)

B3y = -4*pi*10^-7*9/(2*pi*2.75) = -6.54*10^-7 T

Bx = B1 + B2 + B3 = 2.6*10^-7 T

By = B1y + B2y + B3y = -12.36*10^-4 T

magnitude = B = sqrt(B^2 + By^2) = 12.6*10^-7 T <<<_--------ANSWER

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