Line Integral Help

[aprilcm]

Can anyone explain to me why this is true?

 

[topsquark]

This assumes that B is not a function of s! It also assumes that C is a circle centered about a line source of current. Please make sure to post the whole question! (For those that didn't catch that, this is a well known problem about the magnetic field around a line current. The problem uses Ampere's Law.)

$\displaystyle \int_C \dfrac{\vec{B} \cdot \vec{B}}{B}~ds = \int_C \dfrac{B^2}{B}~ds = \int_C B~ds = B \int_C ds$ as I've mentioned elsewhere.

Now, your contour C is a circle of radius r, and $\displaystyle C = 2 \pi r$, thus $\displaystyle ds = dC = 2 \pi dr$.

I haven't left much, but can you finish on your own?

-Dan