(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A square of edge a lies in the xy plane with the origin at its center. Find the value of the magnetic induction at any point on the z axis when a current I' circulates around the square.

2. Relevant equations

B=u/4pi * lineint[(I'*ds' x R)/R^3)]

3. The attempt at a solution

I guess you've got the 4 different sides of the square, I assumed by "circulating" it meant it goes around, so opposite sides the current is going opposite directions. The way I did this, let's say it's going around counter-clockwise, for the side on the right running parallel to the x axis with the current travelling in the positive x direction...

(capital letters = unit vectors)

ds'=dx'X

R=-x'X-a/2Y+zZ

ds' X R = -(zY+a/2*Z)dx'

R^3 = (x'^2+a^2/4+z^2)^(3/2)

so when I integrate that, I'm just gonna say k=uI'/4pi and...

-k{4a(zY+a/2Z)sqrt(2)/[sqrt(a^2+2z^2)*(a^2+4z^2)]}

is my approach even right? I carefully repeated that for all 4 sides and added them, but didn't get the right answer(I don't have the "answer" per se, rather just the value in the middle of the square, which I didn't get right)

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# A magnetic induction question

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