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homomorphism
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Homework Statement
a long hairpin is formed by bending a piece of wire. if the wire carries a current i = 1.15 A.
the figure looks like this:
\subset
point a is at the center of the semicircle part (so that there is a radius r from a to the outside of teh semicircle. i flows counterclockwise. the point b is in the middle of the two parallel lines.
a) what are teh magnitude and direction of \vec{B} at point a?
b) at point b, very far from a?
Homework Equations
\vec{B}_{wire}=\frac{\mu_{0}i}{2d\pi}
where d = r in this case.
\vec{B}_{semicircle}=\frac{\mu_{0}i}{4d}
\oint{\vec{B}\cdot d\vec{s}=\mu_{0}i}
The Attempt at a Solution
I know that I have to add up the contributions of the semicircle, and the two wires to get the total magnetic field at a. However, when i looked at teh solution to part a, they say that each wire contributes \frac{1}{2}\vec{B}_{wire}=\frac{\mu_{0}i}{4d\pi}. I understand teh contribution of the semicircle. how come the total contribution the wires is not 2\vec{B}_{wire}=\frac{\mu_{0}i}{d\pi} ?? This seems to be the magnetic field contribution from both wires for part b) though. does this have to do with how they enclose the wires in an amperian loop?
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