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 \[\overrightarrow{B}\](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)

Correct Answer: D

Solution :

Emf induced when a loop rotates in a magnetic field is \[(e=Ns\,\,B\,\,\omega \sin \,\,\cot ),\] 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 \[t=\frac{3T}{4}\] 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].