KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A semicircular loop of radius R is rotated about its straight edge which divides the space into two regions one having a uniform magnetic field B and the other having no field. If initially the plane of loop is perpendicular to \[\vec{B}\] (as shown), and if current flowing from O to A be taken as positive, the correct plot of induced current v/s time for one time period is





    Correct Answer: D

    Solution :

    Emf induced when a loop rotates in a magnetic field is \[(e=Ns\,\,B\,\,\omega \,\,\sin \,\,\omega t),\] which is a sinusoidal function. Therefore, induced current will also be sinusoidal as shown:
    The curve will be negative, because initially the flux decreases from t=0 to T/4 and then increases from to \[t=\frac{3T}{4}\] to \[\frac{T}{4}.\]
    But from \[t=\frac{T}{4}\] to \[\frac{3T}{4},\] there will be no induced current as there is no field on the right side. Hence, the current produced will be as shown:
    Hence [D].

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