Terminal angular velocity of Disc in magnetic field

  • #1
Advay
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Homework Statement
A metallic disc of radius r is made of a material of negligible resistance and can rotate about a conducting horizontal shaft. A smaller non conducting disc of radius a is fixed onto the same shaft and has a massless cord wrapped around it, which is attached to a small object of mass m
as shown. Two ends of a resistor of resistance R are connected to the perimeter of the disc and to the shaft by sliding contacts. The system is then placed into a uniform horizontal magnetic field B
and the mass m is released. Find the terminal angular velocity with which the disc will rotate finally.
(Take r=10cm, a=2cm, R=1100Ω, B=0.2T, m=50gm, g=10m/s2)
Relevant Equations
torque
Image result for A metallic disc of radius r is made of a material of negligible resistance and can rotate about a conducting horizontal shaft
Torque appiled by smaller disc = mga
emf of disc due to B = Bwr2/2
Current I = Bwr2/2R
force = IBr
= Bwr3/2r
torque = rF
= Bwr4/2r

mga = Bwr4/2r
 
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  • #2
Hello @Advay ,
:welcome: !​

Not bad for a first post, but: what is your question ?

If you are soliciting comments/questions:
  • What happened to R ? And B ?
  • Do the dimensions come out right ?
  • Why do you say
Advay said:
torque = rF

 
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