What is the magnetic field at point P in a current loop?

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SUMMARY

The magnetic field at point P in a current loop can be calculated using the formula B=√2μ0i/8pia, where μ0 represents the permeability of free space, i is the current, and a is the length of the conductor. In part b of the problem, the contributions from the sections of the wire where the current is directed toward or away from point P do not affect the magnetic field due to the cross product being zero. The total magnetic field at point P is determined by summing the contributions from the remaining wire sections, taking into account their geometrical similarities and the inverse square relationship of the magnetic field strength.

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Homework Statement


A current is in a straight conductor of length a.
a. Show that the magnitude of the magnetic field at point P is B=√2μ0i/8pia .
b. Use the result of part a. to find the magnetic field at point P in the current loop below
(magnitude and direction).

http://postimg.org/image/toaspcmfl/
[url=http://postimg.org/image/toaspcmfl/][img=http://s16.postimg.org/toaspcmfl/Untitled.jpg][/url]

Homework Equations



B=√2μ0i/8pia

The Attempt at a Solution



I have part a, its just that I am having trouble going about part b, any help?
 
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Well, the two sections of the wire where the current points directly toward or away from P aren't going to matter, right, since i X r is zero. For the other sections, youre going to just add up the fields from each wire. You found the field for one of them in part a, and the others have similar geometries so they shouldn't be too bad. Remember that the B field goes as 1/r2!
 

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