#### transgalactic

##### Banned

https://i27.tinypic.com/14tsro1.gif

a thin ring with uniform resistance [latex]\rho[/latex]

with radius [latex]r_0[/latex] connected to current I.

the ring is divided into two areas.

calculate the total magnetic field in the center

by current divider:

[latex]I_1=I\frac{l_2}{l_1+l_2}\\[/latex]

[latex]I_2=I\frac{l_1}{l_1+l_2}\\[/latex]

by biot savart law :

[latex]dB=\frac{\mu _0 I ds\times \hat{r}}{4\pi r^2}\\[/latex]

[latex]B_1=\int_{0}^{l_1}\frac{\mu _0 I ds }{4\pi r^2}(+\hat{k})\\[/latex]

[latex]B_2=\int_{0}^{l_2}\frac{\mu _0 I ds }{4\pi r^2}(-\hat{k})[/latex]

[latex]B=B_1+B_2[/latex]

and this is the formal solution

https://i29.tinypic.com/2moc8ds.jpg

they have r^3 in the denominator

why??

the crosst prodct of ds with r is 1

why they take cross product of theta with r??

i cant understand the solution

how they built this integral

??