Need to find dl and r of L6 and L5. Please use the exmple provided for the find

Question

Need to find dl and r of L6 and L5.

Please use the exmple provided for the find dl.

dl= { meter*sin(pi/6) x^ + meter *cos(pi/6) y^ + 0 z^ } - { meter *cos(pi/6) x^ + meter *sin(pi/6) y^ + 0 z^}

= meter *(cos(pi/6)-sin(pi/6)) x^ + meter *(cos(pi/6)-sin(pi/6)) y^ + 0z^ = meter x^ + meter y^ + 0 z^

What is al of L5? What is dl of L6? What istof L5? What is r of L6 The current of the loop is in the X-Y plane L3 L2 L-1 loop_x (m) loop y (m)Zis Zero label 5 L6 1.001368362 -1.731260062 0.99828866891.733037718

Explanation / Answer

from the given diagram
dl will be the difference of adjacent vertices of the hexagon
dr will be the location of the midpoint of this side

for L5 and L6
side of the hexagon = a
a + 2acos(pi/3) = 2
a(1 + 2cos(pi/3)) = 2
a = 1 m
coordinates of 4 = (-1,0)
coordiantes of 5 = (-1 + 1cos(pi/3), -1sin(pi/3) ) = (-0.5, -0.86)
coordinates of 6 = (0.5,-0.86)

hence
dl for L5 = (-0.5 - (-1), -0.86 - 0) = (0.5 , -0.86)
r for L5 = ((-0.5 - 1)/2,(-0.86 + 0)/2) = (-0.75, -0.43)

dl for L6 = (0.5 - (-0.5),-0.86 - (-0.86)) = (1,0)
r for L6 = ((-0.5+0.5)/2,(-0.86 - 0.86)/2) = (0,-0.86)

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