Bending Wires and Magnetic Fields?

AI Thread Summary
The discussion revolves around a test question involving the magnetic fields generated by bent wires, with a focus on solving it quickly without calculators. Participants suggest using the Biot-Savart law but express doubts about its feasibility within the time constraints. The consensus is that only the vertical components of the magnetic field influence the center point, while symmetry indicates that the magnetic field from a half wire is half that of a full wire. This reasoning simplifies the problem significantly. The conversation emphasizes the importance of quick reasoning and symmetry in solving magnetic field problems efficiently.
albert1993
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Homework Statement



see attached. this question is from a test that doesn't allow any calculators and usually makes students solve the problem in 1 minute max.

Homework Equations



perhaps biot savart is to be used? but I doubt that can be done in the time limit...

The Attempt at a Solution



Only the verticals affect the center? I don't know...
 

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Only the verticals affect the center. For the horizontals, by simple symmetry arguments would you agree that the magnetic field due to a half wire will be half that of a full wire? If so, then you are done!
 
Thank you!
 

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