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 c2 = a2 + b2 - 2 a b cosθ.
c2 = a2 + b2 - 2 a b cosθ.
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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