# Magnetic field at the center of a star

1. Nov 3, 2014

### liquidgld9

1. The problem statement, all variables and given/known data

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
2. Relevant 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

3. 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.

#### Attached Files:

• ###### Imagine a giant star.docx
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Last edited: Nov 3, 2014
2. Nov 8, 2014