A solid cylinder of mass m, length l and radius R, is placed on two horizontal parallel
rails of separation l. The cylinder carries a constant current i. A uniform magnetic field
B~ , directed vertically upwards, is switched on. After travelling a distance a, its speed is
(assume rolling without slipping)
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Speed of the centre of mass of the solid cylinder is [2BiLa / m]^0.5 m/s.
The force on a body due to a current through it and a perpendicular magnetic field is:
F = BiL
Hence force on the cylinder is BiL. Given that the mass of the cylinder is m, it's acceleration (A) is:
A = F / m
A = BiL / m
Given that the body has travelled a distance 'a', it's final speed is calculated using the laws of kinematics as follows:
Speed (u) = [2 x A x a]^0.5
u = [2BiLa / m]^0.5 m/s
The force on a body due to a current through it and a perpendicular magnetic field is:
F = BiL
Hence force on the cylinder is BiL. Given that the mass of the cylinder is m, it's acceleration (A) is:
A = F / m
A = BiL / m
Given that the body has travelled a distance 'a', it's final speed is calculated using the laws of kinematics as follows:
Speed (u) = [2 x A x a]^0.5
u = [2BiLa / m]^0.5 m/s
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