Strength of a magnetic field around a wire with current

AI Thread Summary
The discussion revolves around calculating the magnetic field strength at point P due to three parallel wires carrying currents. Two wires have a current of 5.00×10^-4 A flowing toward the observer, while the third wire has a current of 7.50×10^-4 A flowing away. The magnetic field contributions from each wire must be calculated using the formula involving the permeability of free space and the distance from the wires. The user initially attempted a simple addition and subtraction of the magnetic fields but was advised that vector addition is necessary due to the directions of the fields. Accurate vector representation and angle consideration are crucial for determining the correct magnetic field strength at point P.
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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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