Strength of a magnetic field around a wire with current

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Homework Help Overview

The problem involves calculating the strength of the magnetic field at a specific point due to three parallel wires carrying currents in different directions. The setup is a partial square configuration with defined current values and distances.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the magnetic field contributions from each wire using a formula involving the permeability of free space and the distance from the wire. Some participants suggest considering the vector nature of the magnetic fields and the correct direction of each vector at point P.

Discussion Status

The discussion is ongoing, with participants exploring the vector addition of magnetic fields. There is recognition that simple arithmetic may not suffice due to the angles involved in the vector addition process.

Contextual Notes

Participants question the influence of the arrangement of the wires and the opposing currents on the resultant magnetic field, indicating potential complexities in the interactions between the fields generated by the wires.

gigli
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Homework Statement


Three parallel wires are arranged in a partial square configuration with point P as the fourth corner. In two of the wires at opposite corners of the square, a 5.00×10^-4 A current flows toward you, and in the third wire opposite the point P, a 7.50×10−4 A current flows away from you. The sides of the square are 5.36cm. What is the strength of the magnetic field at the point P, at the "missing corner" of the square? (T)

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Homework Equations


I believe I should be using:
(Magnetic field)=[(Permeability of free space)*(current)]/[2*pi*(distance from wire)]
The permeability of free space = (4*pi*10^-7)


The Attempt at a Solution


B1+B2-B3=BP
[(5E-4)((4*pi)E-7)]/(2*pi*.0536) = B1 = B2 = 1.9788436E-9 T

distance from wire3 and point P = r = sqrt(.0536^2+.0536^2) = .0758018469 m
[(7.5E-4)((4*pi)E-7)]/(2*pi*r) = B3 = 1.97884361E-9 T

So, B1+B2-B3 = 1.752E-9 T
which is not correct unfortunately. Do the parallel wires do something weird I am unaware of? I thought only the distance from the wire and the current determined the magnitude of the magnetic field, and the opposing currents caused opposing magnetic fields. Help!
 

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It might help to indicate the B-field vectors at P, due to each individual wire. Be sure to draw each vector in the correct direction.
 
I am still having trouble solving this one. Anyone have any advice?
 
It's vector addition, where you must account for the angles of the vectors (B1, B2, and B3) you are adding up.

Simple addition & subtraction (i.e. "B1+B2-B3") does not work here.
 

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