Torque on cylinder due to current in loop

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SUMMARY

The discussion focuses on calculating the minimum current required to prevent a cylinder from rolling down an inclined plane in a magnetic field. The cylinder has a mass of 3.38 kg, a radius of 5.20 cm, and is wrapped with 70 turns of wire. The magnetic field strength is 0.34 T, and the incline angle is 22.0 degrees. The torque equation used is Torque = IABsin(theta), where I is the current, A is the area of the loop, and theta is the angle between the magnetic field and the current.

PREREQUISITES
  • Understanding of torque and its calculation in physics
  • Familiarity with magnetic fields and their effects on current-carrying loops
  • Knowledge of free body diagrams and forces acting on objects
  • Basic algebra for solving equations involving torque and current
NEXT STEPS
  • Calculate the area of the wire loop using the cylinder's dimensions
  • Determine the torque due to the weight of the cylinder on the incline
  • Explore the relationship between current, torque, and magnetic fields in detail
  • Review examples of similar problems involving magnetic torque and inclined planes
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Students studying physics, particularly those focusing on electromagnetism and mechanics, as well as educators looking for practical examples of torque in magnetic fields.

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Homework Statement


The figure shows a cylinder of mass 3.38 kg, radius 5.20 cm and length 8.12 cm with 70 turns of wire wrapped around it lengthwise, so that the plane of the wire loop is parallel to the incline and contains the axis of the cylinder. What is the least current which while flowing through the loop will prevent the cylinder from rolling or sliding down the inclined plane in the presence of a vertical magnetic field of B = 0.34 T? The angle of inclination http://lon-capa.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char12.png = 22.0 degrees. The plane of the windings is parallel to the inclined plane. You should assume that the wires are wound much tighter than the figure implies (ie, assume that the wire loop has the same dimensions as the cylinder).

CylinderOnInclinedPlane.jpg

Homework Equations


Torque= IABsin(theta)

The Attempt at a Solution



I know I need to find the current so the net torque equals zero. I am confident that the torque due to a current is IABsin(theta). However I can't figure out what the torque due to the cylinders weight or friction might be. Any help would be greatly appreciated.
 
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