How Does a Semicircular Wire Affect Magnetic Field Direction and Magnitude?

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SUMMARY

The discussion focuses on calculating the magnetic field at the center of a semicircular wire using the Biot-Savart law. The magnetic field's magnitude at point P, located at the center of the semicircle with radius 'a' and carrying current 'I', can be derived from the law. Additionally, the direction of the magnetic field at point P is established to be into the page, based on the right-hand rule applied to the current's flow.

PREREQUISITES
  • Understanding of the Biot-Savart law
  • Knowledge of magnetic field direction using the right-hand rule
  • Familiarity with current-carrying conductors
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the Biot-Savart law in detail
  • Learn about magnetic field calculations for different wire shapes
  • Explore applications of the right-hand rule in electromagnetism
  • Investigate the effects of varying current on magnetic field strength
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in understanding magnetic fields generated by current-carrying conductors.

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Homework Statement



Part of a long wire is bent into a semicircle of radius a, as in the figure . A current I flows in the direction shown.
a.)Use the Biot-Savart law to find the magnitude of the magnetic field at the center of the semicircle (point P).

b.) Find the direction of the magnetic field at the center of the semicircle (point P).

The magnetic field is directed to the right.
The magnetic field is directed to the left.
The magnetic field is directed into the page.
The magnetic field is directed out of the page.

Homework Equations


RW-26-62.jpg



The Attempt at a Solution


I tried multiple attempts but I am not sure what I am doing wrong, can someone help??
 
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