Q.8 A metallic rod of length L, is rotating with an angular
frequency w about its one end. Find out the induced emf
produced between the ends of the rod
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Q.8 A metallic rod of length L, is rotating with an angular
frequency w about its one end. Find out the induced emf
produced between the ends of the rod
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Answer:
All points on the rod are moving perpendicular to the magnetic field. Hence, all elementary small elements of the rod induce a small potential difference and the net potential difference in the rod is the integration of the potential differences along the rod.
Motional emf in a conductor moving perpendicular to the field is given by:
ε=Bvl
The potential difference across a small element of rod at a distance l from the center, dε=Bv(dl)
But v=ωl⟹dε=Blωdl
Hence total emf produced across the rod,
ε=∫
0
L
B(lω)dl
=
2
1
BωL
2