• # 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 A) B) C) 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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