Finding the magnetic field at center of a square loop

[lonewolf219]

My textbook says that at the center of a square conducting wire of length ω, the magnetic field is:

B=$\sqrt{2}$μ$_{0}$I/($\pi$R)

I am not sure how to calculate this...?

Because the Biot Savart law has a closed loop integral, we do not use piecewise addition of line integrals to find the magnetic field, as we would to find the magnetic force, is that correct? Do we treat the square loop as if it were a straight wire of total length 4ω?

 

[lonewolf219]

I think we can find the B field for one length of the square and then multiply by 4, because each side contributes the same magnitude. This is because each side is the same length, and each corner makes the same angle with respect to the test point, which would be a 45 degree angle...?

 

[Philip Wood]

You are right. R = (1/8) x perimeter of square.

 

[lonewolf219]

Thanks for the post, Philip Wood!