Use of Biot-Savart Law for Square Loop

[Sekonda]

Hey,

My question concerns the integration of the biot savart law of a differential magnetic field element to find the magnetic field at the center of a square loop. The question is part (c) (using info from (b)) of the image below:

I want to check if what I did was right, but what I did was to integrate the differential magnetic field element separately for each of the 4 sides, using the fact the angle varies between 45 and -45 degrees for each side. So basically I multiplied the integral of the differential magnetic field by 4 and integrated across the limits of 45 degrees and -45 degrees to attain:

$$B=\frac{\sqrt{2}\mu _{0}I}{\pi a}$$

Is this right?

Many thanks for any help/comments!
SK

 

[tiny-tim]

Hey Sekonda!

Yup, looks ok.

(btw, [3] is the differential form of the usual (µ_o/4πa)(sinθ₁ - sinθ₂), = µ_o/2πa for an infinite straight wire )

 

[Sekonda]

Cheers thanks, and so it is; I always miss the ''intricate'' relations between scenario's in electromagnetism.

Thanks again,
SK