the number in red is incorrect 8. The drawing shows an end-view of three wires.

Question

the number in red is incorrect

8. 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 - 12.5 m, b -8.00 m). The current (I) is going out of the page and it is equal to 16.0 A, the current (I2) is going into the page and it is equal to 9.50 A, and the current (Is) is going out of the page and it is equal to 9.50 A. What is the magnitude of the magnetic field at point (P), which is located half way between wire (2) and wire (3)? X9.88e-5 T

Explanation / Answer

magnetic field due to I2 and I3 is additive and in downward direction

B2 = Uo*I2/(2*pi*b/2) = 2*10^-7*9.50/(4) = 4.75*10^-7 T

B3 =  Uo*I3/(2*pi*b/2) = 2*10^-7*9.50/(4) = 4.75*10^-7 T

so total field due to I2 and I3 at midpoint p = 9,50*10^-7 T in downward direction

NOW magnetic field due to I1 is in horizontal direction

B1 = Uo*I1/(2*pi*d)

where d = (a^2 - (b/2)^2)^0.5 = ( 12.5^2 - 4^2 )^0.5 = 11.84 m

=> B1 = 2*10^-7*16/(11.84) = 2.70*10^-7 T

SO net magnetic field at P = 10^-7*[(9.50)^2 + (2.70)^2 ]^0.5 = 9.876*10^-7 T

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