Magnetic field due to currentHard
Question
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 = 10 cm, a = 2 cm, R =
Ω, B = 0.2 T, m = 50 gm, g = 10 m/s2)
(Take r = 10 cm, a = 2 cm, R =
Ω, B = 0.2 T, m = 50 gm, g = 10 m/s2)Options
A.200 rad/s
B.300 rad/s
C.100 rad/s
D.10 rad/s
Solution
At terminal stage, torque applied on smaller disc by rope = mga
current to the disc =
(where ω is terminal angular velcity)
torque applied by magnetic field =
So, = mga
ω = 100 rad/sec
current to the disc =
(where ω is terminal angular velcity) torque applied by magnetic field =
So,
= mgaω = 100 rad/sec
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