How do I calculate the torque of an eddy current brake?

In summary, the conversation discusses the calculation of the torque on an electromagnetic "eddy current" brake, where a disc of conductivity \sigma and thickness d is rotating about an axis and a uniform B field is applied. The torque is given by \sigma*W*d*[B*P*a]^2, and the conversation delves into the steps and factors involved in this calculation. There is also a mention of finding the charge enclosed in a small region of volume d*a^2, which is causing difficulty for the person seeking help.
  • #1
EricVT
166
6

Homework Statement



An electromagnetic "eddy current" brake consists of a disc of conductivity [tex]\sigma[/tex] and thickness d rotating about an axis passing through its center and normal to the surface of the disc. A uniform B is applied perpendicular to the plane of the disc over a small area a^2 located a distance P from the axis. Show that the torque tending to slow down the disc at the instant its angular speed is W is given approximately by [tex]\sigma[/tex]*W*d*[B*P*a]^2

The Attempt at a Solution



I assume that you need to calculate the force on the disc at the small section a^2 and then from this a torque can be easily found. Can you say:

[tex]F=q\cdot(E+v \times B)[/tex]

And since the electric field is motional make this

[tex]F=q\cdot(E+v \times B)=q\cdot(v \times B+v \times B)=q\cdot(2v \times B)[/tex]

[tex]v \times B = BPW[/tex]

[tex]F=2qBPW[/tex]

If so, how do you find the charge enclosed inside of the little region of volume d*a^2? I don't quite see how the conductivity plays into all of this, or where the second factor of B comes from in the solution.

Any help would be appreciated.
 
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  • #2
I'm bumping this (I hope there's nothing wrong with me doing so). I'm having the exact same problem as well.
 
  • #3
Anyone? This problem is due soon, and I'm having trouble getting beyond that point.
 

What are eddy currents?

Eddy currents are swirling currents of electricity that are induced in a conductive material when it is exposed to a changing magnetic field. They are circular in nature and flow in a direction that is perpendicular to the magnetic field.

How are eddy currents produced?

Eddy currents are produced when a conductive material, such as metal, is exposed to a changing magnetic field. This can occur when the material is moving relative to a magnetic field, or when the magnetic field itself is changing.

What is the significance of eddy currents?

Eddy currents have various practical applications, such as in electrical transformers, induction cooktops, and magnetic levitation trains. They can also cause unwanted heating and energy losses in electrical devices.

How do eddy currents affect torque?

Eddy currents can create a torque on a conductive material that is exposed to a changing magnetic field. This is because the circular motion of the eddy currents creates a force that opposes the original motion of the material, resulting in a torque.

How can eddy currents be minimized or controlled?

To minimize the effects of eddy currents, materials with high electrical resistivity are often used. In addition, laminating or layering materials can also reduce the circulation of eddy currents. In some cases, eddy current damping can also be used to control the effects of eddy currents.

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