Why Do Moments Balance in a Faraday Disk but Not the Forces?

• FabJohnson
In summary, the problem involves a conductive disk with a radius of 20 cm rotating around its horizontal axis in a magnetic field of 0.75 T. The disk is connected to a circuit with an e generator and a resistance of 0.3 Ohm. Under steady conditions, the disk rotates at an angular velocity Omega and lifts a mass connected to its edge. The task is to calculate the current in the circuit and the angular velocity Omega. The book uses a formula that equates the moment of weight force to the moment of force from the magnetic field. However, more information and work is needed before any further assistance can be provided.
FabJohnson
Moved from a technical forum, no template.
Hi to everybody! Please: can you help with this problem?
A conductive disk with a radius a = 20 cm, with negligible moment of inertia, rotates around its horizontal axis. The disc region around the radius is inserted in a magnetic field B = 0.75 T perpendicular to the disk itself. A mass is connected to the edge of the disc using a thin wire. The disk is connected to a circuit with an e generator. m. f. = 10 V. The overall resistance of the circuit is R = 0.3 Ohm. Under steady conditions, the disc rotates at an Omega angular velcoity, raising the mass. Calculate: a) the current of the regime that runs through the circuit and b) the angular velocity Omega.
My book calculates the current by the following relation:
mga=iB(a^2)/2 that is: the moment of weight force is equal to the moment of force obtained by the magnetic field. My question is: Why you can't establish the same relation between the forces?
I mean: mg=iBa. It's obviously another result, but I mean: why forces aren't equal, but the moments are?

You will have to show us more of your work before our homework helpers will help.

Forget what the book says, how would you solve the problem?

sophiecentaur

1. What is a Faraday disk with a mass?

A Faraday disk with a mass is an electromechanical device invented by Michael Faraday that is used to generate electricity through electromagnetic induction. It consists of a copper disk with a large number of radial spokes attached to a central axle, and is typically immersed in a magnetic field.

2. How does a Faraday disk with a mass work?

A Faraday disk with a mass works by rotating the copper disk within a magnetic field. This creates a changing magnetic field that induces an electric current in the disk. The current is then collected by brushes attached to the central axle and can be used as a source of electricity.

3. What is the purpose of the mass in a Faraday disk?

The mass in a Faraday disk serves to increase the generator's rotational inertia, allowing for a more stable and continuous output of electricity. It also helps to maintain a consistent speed of rotation, which is necessary for efficient electricity production.

4. What are the advantages of using a Faraday disk with a mass?

One advantage of using a Faraday disk with a mass is that it can generate electricity without the need for a separate power source, making it a self-sustaining device. It is also relatively simple to construct and can be used in a variety of applications, such as in generators and electric motors.

5. Are there any limitations to using a Faraday disk with a mass?

One limitation of using a Faraday disk with a mass is that it can only generate electricity when in motion, so a continuous source of rotational energy is needed to maintain its output. It also has a limited power output compared to other forms of electrical generators, making it more suitable for low-power applications.

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