Joining two wires, magnetic fields and a little algebra

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SUMMARY

The discussion focuses on calculating the magnetic field strength between two parallel wires carrying current, specifically using the formula B = μ iD / π(D² − d²). Participants reference key equations such as B = μ i / 2π d and a trigonometric identity (D² − d²) = (D + d)(D - d) to derive the magnetic field. The conversation highlights the need for clarity in applying these formulas to solve the problem effectively.

PREREQUISITES
  • Understanding of magnetic fields and their calculations
  • Familiarity with algebraic manipulation and trigonometric identities
  • Knowledge of current flow in parallel wires
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of the magnetic field due to parallel wires using Ampère's Law
  • Explore the application of the Biot-Savart Law in calculating magnetic fields
  • Investigate the effects of varying distances on magnetic field strength
  • Learn about the implications of magnetic fields in electrical engineering applications
USEFUL FOR

Students in physics, electrical engineers, and anyone interested in understanding the principles of magnetism and current interactions in parallel conductors.

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Homework Statement


Consider a general point on the line joining the two wires and a distance d
away from the mid-point O. By summing the magnetic field due to currents of magnitude i flowing in both the wires which are non-zero, show that on the line joining the two wires, the magnetic field strength is given by:

B= μ iD / π(D2 −d2)

Homework Equations


(D^2 −d^2) = (D+d)(D-d) ****** a simple trig identity
B= μ i / 2π d

The Attempt at a Solution


I'm kinda stuck - any pointers on where to start?
 
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Just bumping it back up - anyone any ideas?
 

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