Torque on cylinder due to current in loop

In summary, the problem involves a cylinder with certain dimensions and a wire loop wrapped around it, placed on an inclined plane in the presence of a vertical magnetic field. The goal is to find the minimum current needed to prevent the cylinder from rolling or sliding down the incline. The torque equation for this situation is given, but the torque due to the weight and friction of the cylinder is unknown. A free body diagram may help in solving the problem.
  • #1
Rabbittt
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0

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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  • #2
Draw a free body diagram.
 

1. What is the torque on a cylinder due to current in a loop?

The torque on a cylinder due to current in a loop is the rotational force that is exerted on the cylinder when an electric current flows through a loop of wire surrounding it. This torque is caused by the interaction between the magnetic field created by the current and the magnetic field of the cylinder.

2. How is the torque on a cylinder due to current in a loop calculated?

The torque on a cylinder due to current in a loop can be calculated using the formula T = NIAB, where N is the number of turns in the loop, I is the current flowing through the loop, A is the area of the loop, and B is the magnetic field strength at the center of the loop.

3. What factors affect the torque on a cylinder due to current in a loop?

The torque on a cylinder due to current in a loop is affected by the number of turns in the loop, the strength of the current, the size of the loop, and the strength of the magnetic field. Additionally, the orientation of the loop in relation to the cylinder can also affect the torque.

4. How does the direction of the current in the loop affect the torque on the cylinder?

The direction of the current in the loop has a significant impact on the direction of the torque on the cylinder. If the current flows in the same direction as the magnetic field of the cylinder, the torque will be in the same direction as the magnetic field. If the current flows in the opposite direction, the torque will be in the opposite direction.

5. What are some real-world applications of torque on a cylinder due to current in a loop?

One common application of torque on a cylinder due to current in a loop is in electric motors, where this force is used to rotate the cylinder and generate mechanical motion. This principle is also used in devices such as generators and transformers. Additionally, the concept of torque on a cylinder due to current in a loop is important in understanding the behavior of electric currents in circuits and in the development of new technologies.

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