Magnetic field by a finite section of wire?

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SUMMARY

The discussion centers on calculating the magnetic field at the center of a semicircular loop formed by two perpendicular straight wires carrying a current of 6 A. The user correctly identifies the magnetic field contribution from the semicircular section but struggles with the finite wires, specifically the angles involved in the calculation. The integral formula used is μ₀I/4πR (sin φ₁ + sin φ₂), where φ₁ and φ₂ represent the angles from the wires to the center. The confusion arises from determining the correct angles, with the user questioning why 45 degrees is used instead of the expected 0 and 90 degrees.

PREREQUISITES
  • Understanding of magnetic fields generated by current-carrying conductors
  • Familiarity with the Biot-Savart Law
  • Knowledge of angle measurement in the context of magnetic field calculations
  • Basic proficiency in calculus for evaluating integrals
NEXT STEPS
  • Study the Biot-Savart Law and its application to finite wires
  • Learn how to calculate magnetic fields from semicircular loops
  • Explore the concept of vector components in magnetic field calculations
  • Investigate the significance of angle selection in magnetic field equations
USEFUL FOR

Physics students, electrical engineers, and anyone interested in electromagnetism and magnetic field calculations.

helpmeplz!
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hey guys i have a question. i solved the problem but i don't understand how to do it.

Two perpendicular straight wires join in the ends of a semicircular loop of radius a = 11 cm, as shown in the figure above. If the current I =6 A, what is the resultant field at the center of the circular section?

http://gauss.vaniercollege.qc.ca/webwork2/NYBramakko/Magnetic_Field/6/?effectiveUser=0954278&displayMode=images&showOldAnswers=1&user=0954278&key=bIyLRnos5NmBC26Vl4DpQdlatGJalrsW

i know how to get the magnetic field due to the semi circle, but for the two finite wires, i know from the integral we get uo I/ 4piR (sin phi1 + sinphi2). But for me when i look at each section of wire, I see the angles going from 0 to 90 degrees, so phi one is 0 degrees and phi 2 is 90 degree. Doing that gives 0. But that is obviously not right. Why do we use 45 degrees i just don't understand it? Please anyone!
 
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hi helpmeplease! :smile:

your picture is not visible (without logging in) :confused: …

can you please explain the shape (particularly the 45°)? :wink:​
 

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