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imagemania
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Homework Statement
A wire in the shape of semicircle with radius a is oriented in the yz-plane with its center of curvature at the origin (Fig. 28.67). If the current in the wire is I, calculate the magnetic-field components produced at point P, a distance x out along the x-axis. (Note: Do not forget the contribution from the straight wire at the bottom of the semicircle that runs from z = -a to z = +a. You may use the fact that the fields of the two antiparallel currents at z > a cancel, but you must explain why they cancel.)
[PLAIN]http://img560.imageshack.us/img560/7628/capture2fr.png
Homework Equations
Biot & Savot Law
The Attempt at a Solution
Ok I've been attemping this question and managed to get the B(x) part to come out (though as the wrong sign). Thoguh I am struggling to how teh B(y) terms comes out.
From Biot & Savot law B(x) is:
[tex]B_{0} = \frac{\mu_{0}Ia^{2}}{4(x^{2}+a^{2})^{\frac{3}{2}}} [/tex]
I derived this from:
[tex]B_{0} = \frac{\mu_{0}qv\times \hat{r}}{4\pi r^{2}} [/tex]
But b(y) i am unsure about, originally i thought it would be a similar method. But looking at teh solution, it seems to suggest spherical polar coordinates or the use of sin(a)sin(b). Here is the solution:
[PLAIN]http://img17.imageshack.us/img17/5326/capturegpx.png
Can someone help explain to me why this approach is needed for b(y) for the ring (The Rod can simplify to the parallel conudcotrs expression by the looks of it which would be logical). Thanks in advance!
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