Finding Distance Above Long Straight Wire Carrying Current

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SUMMARY

The discussion focuses on calculating the distance (d) above a long straight wire carrying a current of 2.00 µA, where a proton moves parallel to the wire at a speed of 1.90E4 m/s. The magnetic field generated by the current in the wire, as described by Ampère's law, interacts with the proton through the Lorentz force. Gravity also acts on the proton, necessitating a balance between these two forces to determine the value of d. Understanding the interplay between the Lorentz force and gravitational force is crucial for solving this problem.

PREREQUISITES
  • Understanding of Ampère's law and its application in magnetic fields.
  • Knowledge of the Lorentz force equation for charged particles in electromagnetic fields.
  • Familiarity with gravitational force calculations.
  • Basic principles of classical mechanics and electromagnetism.
NEXT STEPS
  • Study the derivation and applications of Ampère's law in electromagnetic theory.
  • Learn the Lorentz force equation and its implications for charged particles in magnetic fields.
  • Explore gravitational force calculations and their relevance in physics problems.
  • Investigate the relationship between electric current and magnetic field strength around a conductor.
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Physics students, educators, and anyone interested in electromagnetism and classical mechanics, particularly those tackling problems involving charged particles in magnetic fields.

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A long straight wire lies on a horizontal table and carries a current of 2.00 µA. In a vacuum, a proton moves parallel to the wire (opposite the current) with a constant speed of 1.90E4 m/s at a distance d above the wire. Determine the value of d. You may ignore the magnetic field due to the Earth.

ok so we have
0.000002 A
19000 m/s proton with mass and charge

the only problem i have is trying to understand what is going on in the problem and what needs to be balanced... once i understand what needs to be equated the physics behind it becomes more apparent... can anyone give me a brief explanation of what needs to be understood to solve this?
 
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The current in the wire creates a magnetic field around the wire as predicted by Ampère's law. There are two forces acting on the proton: Lorentz force (a charged particle in an electromagnetic field) and gravity.
 

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