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fluidistic
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Homework Statement
I must calculate the magnetic field for any point [tex]P[/tex] on an axis passing through the middle of a square wire loop (whose radius is [tex]a[/tex] and current is [tex]I[/tex]).
The situation is such that the square wire is on a plane that is perpendicular to the axis in which I must calculate the magnetic field. If the situation is unclear, please tell it to me so that I scan a sketch of the situation.
Homework Equations
Biot-Savart, despite the symmetry, I don't think that Ampère's law can be useful.
The Attempt at a Solution
I drew a sketch as follow : a horizontal axis (called x-axis) passing in the center of a square with radius [tex]a[/tex]. I drew the square such that its sides coincide with up-bottom-left-right directions, for the sake of simplicity.
Let [tex]\theta (x)[/tex] be the angle measured from the point [tex]P[/tex], between the x-axis and the upper side of the square. I have that [tex]\theta (x)= \frac{a}{2} \cdot \frac{1}{x} \Rightarrow \theta = \arctan \left ( \frac{a}{2x} \right )[/tex].
I've found this angle because I wanted to know the angle within [tex]\vec l[/tex] and [tex]\vec r[/tex] in Biot-Savart law. This is where I'm stuck. Am I in the right direction?
From B-S law : [tex]\vec B =\frac{\mu _0}{4 \pi} I \int d\vec l \times \frac{d \vec r}{r^3}[/tex].
So I wanted to calculate the contribution of each side of the square on the magnetic field situated at point [tex]P[/tex].