Biot-Savart Law with two semi-circles

[Ignitia]

Homework Statement

The accompanying figure shows a current loop consisting of two concentric circular arcs and two perpendicular radial lines. Determine the magnetic field at point P.

Homework Equations

B = μ/(4π) ∫ (I*dl x r)/r²

Btot = Ba - Bb

The Attempt at a Solution

For part a:
Ba = μ/(4π) ∫ (I*a*dθ)/a²
Ba = μI/(4πa) ∫dθ
Ba = μI/(4πa) * π
Ba = μI/(4a)

For part b:

Bb = μ/(4π) ∫ (I*b*dθ)/b²
Bb = μI/(4πb) ∫dθ
Bb = μI/(4πb) * π
Bb = μI/(4b)

So, for Btot = μI/(4a) - μI/(4b) which is only one half of the correct answer. What am I missing?​

 

[Orodruin]

What am I missing?

Nothing, your answer seems correct to me. The double would be the field from two full circular loops with the same current in opposite directions. See, eg., http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html