How Is Torque Influenced by Magnetic Fields in a Rolling Cylinder?

[cliveroth]

[SOLVED] magnetic fields and torque

so for this question, i have an inclined plane with a coil of wire wrapped longitudinally around a cylinder N turns. the plane of the coil is parallel to the inclined plane with a uniform magnetic field they want me to find the least amount of current necessary to prevent the cylinder from rolling down the plane.

im given mass of the cylinder, magnitude of the magnetic field, length of the L portion of the cylinder, & N number of turns.
I am not sure where to start, i have this equation, torque=Ntorque'=NiABsin(phi) where A equals area but I am only give the L part of the cylinder.

i need to have this done by tonight if anyone can help

feel free to lock this thread, i solved the problem

 

[jbsteele]

Ans: The torque caused by the magnetic field is equal to the force of gravity acting on the cylinder. The equation for torque from a magnetic field is NΦBAsinθ, where N is the number of turns, Φ is the flux, B is the magnetic field, A is the area of the coil and θ is the angle between the magnetic field and the normal to the coil.Therefore, we can solve for the current I required to prevent the cylinder from rolling down the plane as I = (mgLsinθ)/(NΦB).

 

[Moetasim]

Hello,

It seems like you have already solved the problem, but I can provide a response for future reference.

To start, we need to understand the relationship between magnetic fields and torque. Torque is a measure of the rotational force acting on an object. In this case, the torque is caused by the interaction between the magnetic field and the current in the coil.

The equation you mentioned, torque = N * torque' = NiABsin(phi), is correct. In this equation, N represents the number of turns in the coil, i is the current in the coil, A is the area of the coil, B is the magnitude of the magnetic field, and phi is the angle between the direction of the magnetic field and the plane of the coil.

Now, to find the minimum current necessary to prevent the cylinder from rolling down the plane, we need to set the torque equal to the torque caused by the gravitational force. This can be represented as follows:

N * torque' = Mgsin(theta) * L

where M is the mass of the cylinder, g is the acceleration due to gravity, and theta is the angle of inclination of the plane.

Solving for i, we get:

i = Mgsin(theta) * L / (NABsin(phi))

So, to prevent the cylinder from rolling down the plane, the minimum current required would be:

i = (mass of cylinder * acceleration due to gravity * sine of the angle of inclination * length of the L portion of the cylinder) / (number of turns * area of the coil * magnitude of the magnetic field * sine of the angle between the magnetic field and the plane of the coil)

I hope this helps. Let me know if you have any further questions. Good luck with your studies!