Terminal angular velocity of Disc in magnetic field

[Advay]

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

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

 

[BvU]

Hello @Advay ,

!​

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

If you are soliciting comments/questions:

• What happened to R ? And B ?$$\quad I = B\omega r^2/2R \quad \&\quad F = IBr \quad = \quad ?? $$
• Do the dimensions come out right ?
• Why do you say

torque = rF

$\$