What happens to the angle between two wires when one current is doubled?

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SUMMARY

The discussion focuses on the effect of doubling the current in one of two parallel wires on the angle between them. The wires, each with a mass of 20 grams per meter, initially create equal angles when carrying equal currents in opposite directions. When one current is doubled, the tension and magnetic forces acting on the wires change, affecting the angles. The key equation involved is F = BIL, which relates force to magnetic fields and current, indicating that the angle will not remain the same after one current is increased.

PREREQUISITES
  • Understanding of electromagnetic forces, specifically the Lorentz force.
  • Familiarity with Newton's laws of motion, particularly the third law.
  • Basic knowledge of trigonometric functions as they relate to forces and angles.
  • Ability to apply the equation F = BIL in practical scenarios.
NEXT STEPS
  • Explore the implications of the Lorentz force on current-carrying conductors.
  • Study the relationship between current, magnetic fields, and tension in wires.
  • Investigate the application of Newton's laws in electromagnetic systems.
  • Learn about the effects of varying current on the equilibrium of forces in physics.
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in the dynamics of current-carrying conductors and their interactions.

Eitan Levy
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Homework Statement


We have two very long wires, each with the same mass of 20 grams per meter. They are hung from the ceiling with two identical wires. When they both had the same current flowing to the opposite directions, they created the same angle.
We double the current in one of them, is the angle that they will create (as shown in the picture) will be the same again?

Homework Equations


F=BIL

The Attempt at a Solution


I couldn't prove it. I am stuck with T1sinθ1=T2sinθ2.
Is there any assumption I am supposed to make? I know that the forces are tension, gravity and magnetic force, and I understand what their directions are.
 
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The picture:
 

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What does Newton's 3rd law say? What does that imply for the two angles? Will they be equal? Will they be the same or larger than before one of the currents was doubled?
 

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