Two infinitely long parallel wires separated by 1 m, 6 m above ground. Find magnetic flux density

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Adam Uraynar

Joined Dec 21, 2015
67
Two infinitely long parallel wires separated by 1 m are at 6 m above ground. Each carries a 60-Hz AC current of 100 amperes (rms), but in opposing directions. Find the magnetic flux density B at a test location on the ground which is at an equal distance from the wires.


As the solution shows, 4.7*sin(377t) micro-Tesla for each wire makes sense. But where are they getting the total B-field equaling 0.78 micro-Tesla?
How are the vertical components calculated? h = 6 m...
B1 = u*i/(2*pi*R)
B1 = 2*10^(-7)/6 = 3.33e-8
 

panic mode

Joined Oct 10, 2011
1,783
B1 and B2 are vectors and article also points that out. each of them can be decomposed into two components - horizontal and vertical.
horizontal components are opposite so cancel each other. vertical components are in same direction and add up.

|B| = 2*|B1|*cos(angle)
where angle = atan(h/(d/2) = atan(2h/d) =85.23 Deg

|B|=2*4.7*cos(85.23) uT

of course this assumes that you understand properties of line and intersection angles.
 
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