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Homework Statement
Picture of the problem:
I first need to calculate the magnetic field in point P caused by the piece of wire at z = R (so the top wire parallel to the y-axis).
Homework Equations
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Biot-Savart law for magnetic fields:
##\vec {dB} = \frac {μ0*I} {4*π} * \frac {\vec {dl} ×\vec {r}} {r^3}##
The Attempt at a Solution
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Here is what I did:
##\vec {dl} = dy * \vec {ey}## (where ey is the unit vector in the y direction)
##\vec r = (P - y)* \vec {ey} - R * \vec {ez}##
then:
##\vec {dl} ×\vec r = -R*dy*\vec {ex}##
so now I can write:
##\vec {dB} = - \frac {μ0*I*R} {4*π} *\frac {1} {(P - y)^2 + R^2)^{3/2}} * dy * \vec {ex}##
Now I can integrate this using the substitution ##u = P-y## and ##du = -dy##, and then integrate from ##-L## to ##0##, which gives me an expression for the magnetic field:
##\vec B =\frac {μ0*I} {4*π*R} *(\frac {P} {\sqrt {P^2+R^2}} -\frac {P+L} {\sqrt {(P+L)^2+R^2}}) * \vec {ex}##
Now this answer is almost correct except there should be a minus in front. However my minus disappeared when I used the substitution ##du = -dy##. Does anyone know where I went wrong?
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