Questions
A rod of length L rotates in the form of a conical pendulum with an angular velocity about its axis as shown in figure. The rod makes an angle with the axis. The magnitude of the motional emf developed across the two ends of the rod is
detailed solution
Correct option is D
ε=∫v⇀×B⇀.dl⇀⇒ϵ=∫[(lsinθ)ω×B(-j∧)].[dlsinθ(-i∧)+dlcosθ(-j∧)]⇒ε=∫Bωl sinθi∧.dl sinθ-i∧+dl cosθ-j∧=-Bωsin2θ∫0Lldl=-12Bωsin2θL2⇒ϵ=Vb-Va=-12BωL2sin2θNegative sign indicates that end b will be negative w.r.t. a.Alternate Method:Consider two more conductors ac and bc. This completes a closed loop. The net emf induced in this closed loop should be zero, as net flux through this loop always remains zero.eab+ebc+eca=0but ebc=12BωL sinθ2,eca=0 putting the values, we geteab=-12BωL sinθ2Similar Questions
An elasticized conducting band r is around a spherical balloon T (figure). Its plane passes through the center of the balloon. A uniform magnetic field of magnitude 0.04 T is directed perpendicular to the plane of the band. Air is let out of the balloon at 100 cm3s-1 at an instant when the radius of the balloon is 10 cm. The induced emf in the band is
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