A) inclined at \[30{}^\circ \] to the magnetic field
B) perpendicular to the magnetic field
C) inclined at \[45{}^\circ \] to the magnetic field
D) parallel to the magnetic field
Correct Answer: D
Solution :
As the coil is rotated, angle \[\theta \] (angle which normal to the coil makes with \[\overrightarrow{B}\] at any instant t) changes, therefore magnetic flux \[\phi \] linked with the coil changes and hence an emf is induced in the coil. At this instant t, if e is the emf induced in the coil, then \[e=-\frac{d\phi }{dt}=-\frac{d}{dt}(NAB\,\,cos\,\omega t)\] where N is number of turns in the coil. or \[e=-NAB\frac{d}{dt}\,\,(\cos \,\,\omega t)\] \[=-NAB(-\sin \,\omega t)\omega \] or \[e=NAB\,\omega \,\sin \,\omega t\] ?..(i) The induced emf will be maximum When \[sin\text{ }\omega \text{t}=maximum=1\] \[\therefore \] \[{{e}_{\max }}={{e}_{0}}=NAB\,\omega \times 1\] or \[e={{e}_{0}}\,\sin \,\omega t\] Therefore, e would be maximum, hence current is maximum (as \[{{i}_{0}}={{e}_{0}}/R\]), when \[\theta ={{90}^{o}},\] i.e., normal to plane of coil is perpendicular to the field or plane of coif-is parallel to magnetic field.
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