A wire loop enclosing as semicircle of radius `R` is located on the boudary of uniform magnetic field `B`. At the moment `t=0`, the loop is set into rotation with a costant angular acceleration `alpha` 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. Draw the approximate plot of this function.The arrow in the figure shows the emf direction taken to be positive.

Explanation

Assume the loop to have entered the field regions , and let angle be `theta`
As the area of the sector shaded is `1/2 a^2 theta`
` phi = B(1/2 a^2 theta) cos 0`
` (dphi)/(dt) = 1/2 a^2 B ((d theta)/(dt))`
`|epsi| = (dphi)/(dt) = (a^2 B omega)/(2)`