Magnetic field due to an uneven current loop

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SUMMARY

The discussion focuses on calculating the magnetic field at point P due to a closed circuit formed by two semicircles with radii of 40 cm and 20 cm carrying a clockwise current of 3.0 A. The participant attempted to apply the formula B = (μ * I) / (2πR) but recognized that this equation is applicable for infinitely long straight wires, not for the configuration of small loops present in this problem. The correct approach requires integrating contributions from each semicircular segment rather than using a single formula for straight wires.

PREREQUISITES
  • Understanding of magnetic field equations, specifically B = (μ * I) / (2πR)
  • Knowledge of the Biot-Savart Law for calculating magnetic fields from current distributions
  • Familiarity with the geometry of semicircles and their contributions to magnetic fields
  • Basic skills in calculus for integrating magnetic field contributions
NEXT STEPS
  • Study the Biot-Savart Law for calculating magnetic fields from current-carrying conductors
  • Learn how to integrate magnetic field contributions from different geometric shapes
  • Explore the concept of magnetic fields due to loops and coils in electromagnetism
  • Review examples of magnetic field calculations for non-linear current paths
USEFUL FOR

Students in physics or engineering, particularly those studying electromagnetism, as well as educators looking for practical examples of magnetic field calculations in complex current configurations.

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Homework Statement


"A closed circuit consists of two semicircles of radii 40cm and 20cm that are connected by straight segments. A current of 3.0 A exists in this circuit and has a clockwise direction. Find the magnetic field at point P (center of the figures).

Homework Equations


B = (mu * I)/(2piR)

The Attempt at a Solution



I had thought adapting the above equation would be the way to go, just using two different radii. I ended up with:

[tex]\frac{1}{2}[/tex][tex]\mu[/tex][tex]\frac{I}{2\pi}[/tex] * [tex]\left(\frac{1}{20} - \frac{1}{40}\right)[/tex]

LaTeX didn't like the above, so in plaintext:

(1/2)(mu0 * I)/(2pi) * (1/20-1/40)

This didn't work, though, and I'm not entirely sure why.
 
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That's the equation for an infinitely long, straight wire. You have two small loops, not two infinitely long wires.
 

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