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A CONDUCTING ROD OF LENGTH L WHOSE ONE END IS FIXED IS ROTATED ABOUT THE AXIS PASSING THROUGH ITS FIXED END AND PERPENDICULAR TO ITS LENGTH WITH CONSTANT ANGULAR VELOCITY w ,MAGNETIC FIELD PERPENDICULAR TO THE PLANE OF PAPER , THEN EMF INDUCED ACROSS THE ENDS OF THE ROD IS 1\2 BwL^2. PLEASE EXPLAIN THE DERIVATION


A CONDUCTING ROD OF LENGTH L WHOSE ONE END IS FIXED IS ROTATED ABOUT THE AXIS PASSING THROUGH ITS FIXED END AND PERPENDICULAR TO ITS LENGTH WITH CONSTANT  ANGULAR  VELOCITY w ,MAGNETIC FIELD PERPENDICULAR TO THE PLANE OF PAPER , THEN EMF INDUCED ACROSS THE ENDS OF THE ROD IS 1\2 BwL^2. PLEASE EXPLAIN THE DERIVATION
 


Grade:10

1 Answers

ROSHAN MUJEEB
askIITians Faculty 833 Points
3 years ago
emf induced,ε=dtdϕ​=dtd​(BA)=BdtdA​wheredtdA​is the rate of change of area of the loop formed by sector OPQ,
Area of OPQ=R2×2πθ​=21​R2θ
ε=B×dtd​(21​R2θ)
=21​BR2dtdθ​=2BωR2​

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