Need to find dl and r of L in the figure provided below. Please use the exmple p

Question

Need to find dl and r of L in the figure provided below. Please use the exmple provided for the find dl.

Show the work please!!!!!!!!! And use Wolfram alpha for Cos(pi/6) for check the trigfunctions, or else answers are going to be incorrect!!!!!!!!!

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 L3? What is r of L3 ? The current of the loop is in the X-Y plane. L3 L2 di3 L-1 al loop x (m)loop. y (m)zis Zero. label 4 1.999999649 0.00118530711

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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