Two parallel power lines separated by a distance of d=4.0 m run h=8.0 m above th
ID: 2140220 • Letter: T
Question
Two parallel power lines separated by a distance of d=4.0 m run h=8.0 m above the ground. The current in each line is I=22 A and flows in the opposite direction as shown in Figure. A person on the ground is below the power lines at the same distance from them. Find the magnitude and the direction of the net magnetic field generated by the two lines at the position where the person stands. For direction, choose one letter indicating the direction shown in Figure. Choose "No direction" if the magnetic field is zero. [Note: In this problem we assume the current is DC but in the real world it should be AC.]Explanation / Answer
Mag field due to a straight wire
B =?0I/2?d (d = distance)
Distance from each wire to the person = d = sqrt(8^2 + 2^2) = 8.246 m
SInce the currents are flowing in the opposite directions, therefore the 2 magnetic fields will have the same magitude but will act in such a way that the horizontal comoponents of the field cancel out and only the vertical components remain.
? B_net = 2 x B_individual x sin? (using inversetangent of 2/8 to find?)
B_individual = (4? x 10^-7 x 22)/(2? x 8.246)
= 5.336 x 10-7T
? B_net = 2 x 5.336 x 10-7x sin(14.036) =2.59 x 10-7Tacting upward perpendicular to the ground
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