Torque on a current carrying wire

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SUMMARY

The discussion focuses on calculating the current required to initiate movement in a 20cm square loop of copper wire placed in a uniform magnetic field of 0.6 T. The loop's diameter is 3mm, and it is resting on a paramagnetic table. The forces acting on the loop are derived from the equation F = I(L × B), where the magnetic force on the loop's sides causes a torque that can overcome friction, which has a coefficient of 0.2. The analysis concludes that the right side of the loop will lift while the left side pushes down, indicating a net torque that initiates movement.

PREREQUISITES
  • Understanding of electromagnetic principles, specifically Lorentz force.
  • Familiarity with torque calculations in physics.
  • Knowledge of the properties of copper, including density and electrical conductivity.
  • Basic understanding of friction and its role in motion.
NEXT STEPS
  • Calculate the exact current required to overcome static friction using F = I(L × B).
  • Explore the effects of varying magnetic field strengths on the torque produced in a wire loop.
  • Investigate the relationship between wire diameter and current-carrying capacity in copper.
  • Learn about the applications of torque in electromagnetic devices, such as motors and generators.
USEFUL FOR

Physics students, electrical engineers, and anyone interested in the principles of electromagnetism and their practical applications in devices involving current-carrying conductors.

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Homework Statement



magfield.png

Consider the 20cm square loop of rigid wire shown in the figure. The wire has a diameter of 3mm and is lying flat on a table made of paramagnetic material. A uniform magnetic field of B=0.6 rans parallel to the table top as pictured. Electrical connection to the thick copper wire is established via two very thin, light leads as shown. The density of copper is 8.96g/cm^3 and the coefficient of friction is 0.2.
What value of current into the loop will cause the loop to start to move?
Describe how the loop will move.

Homework Equations



[itex]\vec{F}=I(\vec{L}\times\vec{B}[/itex]

The Attempt at a Solution


I know that the force on the right hand leg will be directed out of the page, and that the force on the left leg will be into the page. As far as I can tell, the right side of the loop will want to lift off the table, and the left side will want to push into the table. I don't really think that friction will have a play in this. Would we merely apply sum of F=0 on the left leg?
mg=ILBsinx?
 
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The right hand side will begin to lift up, and eventually the force will have a component that opposes the frictional force. I don't know what else to do from here. Sorry
 

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