Magnetic field at the center of a star

[liquidgld9]

Homework Statement

Imagine a giant star, lit with twinkly lights for the holiday season. Are you interested in the magnetic field at the center of the star? Sure you are. The star has “arm” length (AF) equal to 1 m and 1 amp flows clockwise around the star.
1. Find the following lengths:
BG =
FG =
HG=
FH=
2. Find the magnetic field at point H.
(G is midpoint of A and C and H is in the center)
see attached for pic of star

Homework Equations

Magnetic field of wire: $B = \frac{Uo}{4\pi} ∫ \frac{(ids \,X\, R)}{r^2}$

R is the unit vector that points from the differential element to the point of interest
r is the distance between the differential element and the point of interest

The Attempt at a Solution

I think I have the lengths for part 1:
BG = sin (72) = .95
FG = cos(72) = .3
HG= .3tan18 = .95
FH= 1.02

and I think I can find the field from point A-F

$\frac {Uoi}{4\pi} ∫\frac {(ds i) X (-GHj)} { (GH^2 + (AG - s)^2)^3/2}$

(I left out the i component on top because it cancels)

where i and j in the integral are directions, and s is the location of ds starting from A.
solving the integral, i get $-.5 \frac{Uoi} {4\pi} k$

I am not really sure how to set up the integral for the wires like F-B, I tried:
$r = Ssin18 - (BH-Scos18)$
$ds = dsi + dsj$
with s being the distance of ds starting at B.
I don't think that's right, i couldn't solve the integral.
Any help would be greatly appreciated.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[liquidgld9]

Ive come to two conclusions. The first is I miss calculated at least one length in part 1. For part 2, The field in the middle, I think I was making it harder than it needed to be. All lines on the star should create the same magnetic field, in direction and magnitude, so I should only need the field from 1 line, like A-F, and multiply that by the number of sides.