How Is Magnetic Induction Calculated in a Triangle of Parallel Wires?

AI Thread Summary
The discussion revolves around calculating the magnetic induction at the center of an equilateral triangle formed by three parallel wires carrying currents of 10A, 10A, and 20A in different directions. The initial calculations yield magnetic fields B1 and B2 as 2.5 x 10^-5 T and B3 as 5 x 10^-5 T. The user expresses uncertainty about which values to consider and how to combine them correctly based on their directions. After further calculations, the user arrives at a total magnetic induction of 7.423 x 10^-5 T, but notes that the expected solution is 5.1 x 10^-5 T. Clarification on vector directions and the correct application of the formula is sought to resolve the discrepancy.
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Homework Statement


Three parallel wires are put in the angles of an equilateral triangle with sides 14 cm. The values of the currents are 10A,10A, 20A and the first and third are in different directions. Find the magnetic induction in the center of the triangle

Homework Equations


B=I*μ0/2*pi*d

The Attempt at a Solution


B1=B2=2.5*10^-5T
B3=5*10^-5T. I don't know which of these cases should I consider based on the problem's information.
Could you tell me which is right so I can continue with the sketch of induction?
http://postimg.org/image/4aco9wajl/
 
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Doesn't matter:smile: for the magnitude. Do all four if you don't believe me,,,,,
 
BvU said:
Doesn't matter:smile: for the magnitude. Do all four if you don't believe me,,,,,
So here's what I did. http://postimg.org/image/8licrhc1f/
B12=2.5*10^-5T (as the angle is 120 degress), B3=5*10^-5 T. As they are opposite vectors. (5-2.5)*10^-5=2.5*10^-5 T.
 
Check the direction of B3.

Reason for this suspicion: I what would be the situation if all three currents were in the same direction and of equal magnitude ?
 
BvU said:
Check the direction of B3.

Reason for this suspicion: I what would be the situation if all three currents were in the same direction and of equal magnitude ?
http://postimg.org/image/npe8682kp/
I corrected it.
The formula:
B=I*μ0/2*pi*d
B1=B2=2.4743*10^-5 T
B3=4.9486*10^-5 T
B=B12+B3=7.423 -10^-5 T, but the solution is 5.1*10^-5 T.
 
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