Question

A wire loop enclosing a semi-circle of radius a is located on the boundary of a uniform magnetic field of induction B (Fig. 3.80). At the moment t = 0 the loop is set into rotation with a constant angular acceleration β about an axis O coinciding with a line of vector B on the boundary. Find the emf induced in the loop as a function of time t. Draw the approximate plot of this function. The arrow in the figure shows the emf direction taken to be positive.

Answer 1

Flux at any moment of time,

where φ is the sector angle, enclosed by the field. Now, magnitude of induced e.m.f. is given by,

where ω is the angular velocity of the disc. But as it starts rotating from rest at t = 0 with an angular acceleration β its angular velocity ω (f) = βt. So,

According to Lenz law the first half cycle current in the loop is in anticlockwise sense, and in subsequent half cycle it is in clockwise sense.

Thus in general,  where n in number of half revolutions. 

The plot  is shown in the answer sheet.