Electromagnetics = Biot-Savart Law around square path

[satchmo05]

Homework Statement

Find the B-field at the center of the square loop located above the xy plane, with width (w), and current I rotating counter-clockwise.

Homework Equations

Here is the given equation:
B = [(μ_o*I*a_Ф)/(4∏*ρ)](cosα₂ – cosα₁)

The final answer is for the B-field about the loop is:
B = [(4μ_o*I)/(∏*w*(√2))]a_z
How do I obtain this answer? I am having trouble with the angles that I am supposed to use.

The Attempt at a Solution

I used (w/2) for the radial component, ρ. I used 45 degrees for α₂, and 90 degrees for cosα₁, and this is obviously wrong. Which angles do I use to get the correct angle?

 

[satchmo05]

Solving this analytically for cosα₂ - cosa₁, I should receive 2/sqrt(2). How should I set up my angles to achieve this? Thank you for all help, I greatly appreciate it!

 

[kuruman]

What kind of picture goes with the given equation? In other words, for what situation was it derived? How are ρ, α₁ and α₂ defined?