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## Homework Statement

Two long thin parallel wires a distance d = 15.3 cm apart carry 25-A currents (I) in the same direction. The magnetic field is measured at point P, a distance d1 = 13.3 cm from the lower wire and a distance d2 = 5.3 cm from the upper wire.

a. Find the x and y components of the magnetic field at P due to the current in the lower wire only.

HELP: First find the magnitude of the field due to the current in the lower wire.

HELP: To find the direction of the field, the Law of Cosines will be helpful: for a triangle of sides a, b, and c, the angle θ between sides a and b is given by c

^{2}= a

^{2}+ b

^{2}- 2 a b cosθ.

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/Knox/phys130a/spring/homework/13/04/HW14_4.jpg [Broken]

## Homework Equations

c

^{2}= a

^{2}+ b

^{2}- 2 a b cosθ.

Magnitude=[tex]\mu[/tex]

_{0}I/2[tex]\pi[/tex]r

## The Attempt at a Solution

So I found the magnitude to be [tex]\mu[/tex]

_{0}(25)/2[tex]\pi[/tex](.133)=3.759E-5

then I use the Law of Cosines to find that theta=19.814

so then 90-19.814=70.186

Cos of that= y/3.759e-5

which gives me y=1.274e-5

Which is correct.

However, when I use Sin of 70.186=x/3.759e-5 I get 3.536e-5, but this is not correct. I'm not sure what I'm doing wrong here. :/ I've never quite understand how to tell when you use Sin and Cos for which value anyway.

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