How Does a Finite Wire Segment Affect Magnetic Field Calculation?

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SUMMARY

The discussion focuses on calculating the magnetic field produced by a finite wire segment carrying an 8A current along the z-axis. The initial attempt incorrectly applies the formula for an infinite wire, B = μ₀I / 2πR, instead of the appropriate method for a finite wire segment. The correct approach involves integrating the contributions of the magnetic field from each infinitesimal segment of the wire. The final magnetic field at the specified point (0.4m, 0, 0.3m) must consider both magnitude and direction derived from vector analysis.

PREREQUISITES
  • Understanding of Biot-Savart Law for finite wire segments
  • Familiarity with vector calculus and magnetic field direction
  • Knowledge of magnetic permeability (μ₀) and its significance
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the Biot-Savart Law for calculating magnetic fields from finite wire segments
  • Learn how to perform vector integration in the context of magnetic fields
  • Explore the concept of magnetic field direction using right-hand rule
  • Review examples of magnetic field calculations for various wire configurations
USEFUL FOR

Students of electromagnetism, physics educators, and anyone involved in electrical engineering or physics who needs to understand magnetic field calculations for finite wire segments.

Jethom18
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Homework Statement



A long straight wire lies along the z-axis and carries an 8A current in the +z direction. Find the magnetic field (magnitude and direction) produced at x = 0.4m, y = 0, z = .3m by a .7mm segment of wire centered at the origin.

Homework Equations



B = u(0)I / 2piR

The Attempt at a Solution



b = (4(pi)x10^-7) (8A) / (2pi (.7x10^-3) ==> 2.3 mT(tesla)

I think that's right, but I'm not sure where the magnitude and direction with the vectors come in. I'm assuming you subtract vector 1 from origin vector to leave .4i + .3k. Then do you take the magnitude and multiply it by b?

Thanks for any help.
 
Physics news on Phys.org
You didn't use the right equation to find B. B = u(0)I / 2piR is for an infinitely long wire, but the question asks for the field produced by a finite wire segment.
 

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