Why Does the Toroid's Magnetic Field Equation Use a Cubed Distance Term?

[richyw]

Homework Statement

I'm working through a proof that says the magnetic field of a toroid is circumferential at all points inside and outside the toroid. I can follow most of the proof, but am a bit confused where the first equation comes from.

Here is the figure from the textbook (Griffith's 4th Ed).

http://media.newschoolers.com/uploads/images/17/00/67/76/17/677617.jpeg

To begin the proof, Griffiths starts with the field at \mathbf{r} due to the current element at \mathbf{r}'.d\mathbf{B}=\frac{\mu_0}{4\pi}\frac{\mathbf{I}\times\mathbf{\hat{{u}}}}{u^3}dl'

Homework Equations

\mathbf{B}=\frac{\mu_0}{4 \pi}\int\frac{\mathbf{I}\times\mathbf{\hat{u}}}{u^2}dl'

The Attempt at a Solution

I'm just confused at how Griffiths got from the Biot-Savart law above, into the equation he posted in the question. (I replaced the script r with a u). Where does the cubed term come from?

 

[xophergrunge]

I believe that is a mistake in the text. I think he meant it to be the vector r and not r hat, in which case the denominator would be cubed.

 

[rude man]

I agree with post #2. Otherwise the dimensions don't check out.

 

[richyw]

cool thanks. I was thinking that, but I wanted to confirm!