Magnetic Field from two parallel wires

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The discussion focuses on calculating the magnetic field at a point equidistant from two parallel wires carrying the same current. The relevant equations include U0I/2πr and U0I/4πa(cos(theta1) - cos(theta2)), with attempts made to apply these formulas. The user has struggled with various calculations over five days, indicating difficulty in achieving the expected results. It is noted that the magnetic field from each wire is circular and directed clockwise when the current flows into the plane of the paper. A diagram may assist in visualizing the vector nature of the problem.
Geogargoyle
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Homework Statement


Each of two long straight parallel wires separated by a distance of 24.0 cm carries a current of 5.00 A
in the same direction. What is the magnitude of the resulting magnetic field at a point that is 14.0 cm
from each wire?

Homework Equations


U0I/2pir
U0I/4pia(cos(theta) -cos(theta2))
B1 + B2 =B

The Attempt at a Solution


I have tried (U0I/2pir)2 as well as U0I/4pia(cos(theta) -cos(theta2)) Where theta 1 is approx 30 and theta 2 is approx 150. r in both equations have been .14. I have also tried U0I/2pi(.14) + U0I/2pi(.24-.14). And a series of other variations which never yield close to the given potential answers. Been working on this for 5 days now.
 
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The calculation of the magnetic field is solved for each wire separately using Ampere's Law. This is a vector problem and it can help to draw a diagram with the current from the two wires flowing into the plane of the paper. The magnetic field from each wire is in a circular clockwise direction around each wire when the electrical current points into the plane of the paper.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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