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

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Homework Help Overview

The problem involves calculating the magnetic induction at the center of an equilateral triangle formed by three parallel wires carrying different currents. The wires have currents of 10A, 10A, and 20A, with the first and third wires carrying currents in opposite directions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculations of magnetic induction for each wire and question which values to consider based on the problem's setup. There are attempts to clarify the direction of the magnetic fields produced by the currents and how they interact.

Discussion Status

Participants are exploring different calculations and questioning the correctness of their approaches. Some have provided calculations for the magnetic induction values but express uncertainty about the correct interpretation of the results. There is no explicit consensus on the correct approach or final value.

Contextual Notes

Participants are considering the implications of varying current directions and magnitudes, and how these affect the resultant magnetic induction. There is a mention of a potential scenario where all currents are in the same direction, prompting further exploration of the problem's assumptions.

zade70
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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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