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

a long hairpin is formed by bending a piece of wire. if the wire carries a current [tex]i = 1.15 A[/tex].

the figure looks like this:

[tex]\subset[/tex]

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 [tex]\vec{B}[/tex] at point a?

b) at point b, very far from a?

2. Relevant equations

[tex]\vec{B}_{wire}=\frac{\mu_{0}i}{2d\pi}[/tex]

where d = r in this case.

[tex]\vec{B}_{semicircle}=\frac{\mu_{0}i}{4d}[/tex]

[tex]\oint{\vec{B}\cdot d\vec{s}=\mu_{0}i}[/tex]

3. 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 [tex]\frac{1}{2}\vec{B}_{wire}=\frac{\mu_{0}i}{4d\pi}[/tex]. I understand teh contribution of the semicircle. how come the total contribution the wires is not [tex]2\vec{B}_{wire}=\frac{\mu_{0}i}{d\pi}[/tex] ?? 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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# Homework Help: Question about magnetic field of a current

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