How Do Magnetic Fields Interact at Point P Between Parallel Wires?

AI Thread Summary
The discussion focuses on calculating the magnetic field at point P between two parallel wires carrying 25-A currents in the same direction. The user successfully determined the magnitude of the magnetic field from the lower wire but struggled with finding the x-component using sine, while the y-component calculation was correct. Suggestions were made to check for significant figure errors, roundoff mistakes, or sign errors in the final answer. Additionally, the importance of correctly indicating the direction of the magnetic field in diagrams was highlighted. Understanding the application of sine and cosine in this context remains a challenge for the user.
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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 c2 = a2 + b2 - 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

Homework Equations


c2 = a2 + b2 - 2 a b cosθ.
Magnitude=\mu0I/2\pir



The Attempt at a Solution


So I found the magnitude to be \mu0(25)/2\pi(.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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Your work looks pretty good, so I imagine the problem is one of the following:

Wrong number of significant figures in final answer,
Final answer slightly wrong from roundoff error,
or
+/- Sign error in final answer.

In your diagram, have you drawn the direction of B due to the lower wire? That might help clear up whether it's + or -.
 
I didn't even think about the fact that it could be negative. B is going anti-clockwise, so it's negative. Thanks!
 
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