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Fig  shows L-shaped rod rotating about its end O

in a plane perpendicular to the magnetic field B. The part OA of the rod is non-conducting while the part AB is conducting. The induced e.m.f. between the ends A and B is

a
12ωBL2
b
ωBL2
c
2ωBL2
d
12ωB2L

detailed solution

Correct option is A

Consider a small element dx as shown in fig.(22). Here (dx x v) ll B∴eAB=∫0L [dxωrsin⁡θ]B=ωB∫0L xdx [∵rsin⁡θ=x]=12ωBL2

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