CBSE Class 12-science Answered
Please help me with the torque part . How is the direction of the torque in clockwise direction and to keep the rod rotating it must me in anticlockwise direction??
Asked by prakriti12oct | 29 Sep, 2019, 02:25: AM
Expert Answer
induced emf e in the rod , e = -dφ/dt ...........................(1)
where dφ is change in magnetic flux in time dt.
change in magnetic flux dφ = B×dA ............................(2)
where B is magneic field flux density and dA is the angle swept by rod in time dt.
if the rod rotates by angle dθ in time dt, then area dA = (dθ/2π)×πa2 = dθ×(a2/2) ......................(3)
By using eqn.(2) and eqn.(3), eqn.(1) is rewritten as , e = - B × (dθ/dt) ×(a2 / 2 ) = - B×ω×(a2 / 2 )
Current i in the resistance R is given as, i = emf / R = [ B×ω×(a2 / 2 ) ] /R ..............................(4)
Due to current i passing through the rod, a force ia × B is experienced by rod that opposes the motion.
Magnitude of this opposing force = (B×i×a ) = [ B2×ω×a3 ] / (2R)
Hence torque acting on the rod = force × distance = [ ( B2×ω×a3 ) / (2R) ] × a = [ B2×ω×a4 ] / (2R)
whenever a current carrying conductor moves in a magnetic field, magnetic field opposes the motion and
the electromagnetic force ia × B is opposing the anticlockwise movement of the rod.
Hence oppsing torque due to electromagnetic force acting on the rod is in clockwise direction.
We need to apply external torque in anticlockwise direction to overcome the torque due to electromagnetic force.
The rod itself is not rotating in magnetic field, but rotates due to applied external torque.
Answered by Thiyagarajan K | 29 Sep, 2019, 08:36: AM
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