The drawing shows a coil of copper wire that consists of two semicircles joined by straight sections of wire. In part (a) the coil is lying flat on a horizontal surface. The dashed line also lies in the plane of the horizontal surface. Starting from the orientaation in part (a) the smaller semicircle rotates at an angular frequency `omega` about the dashed line, until its place becomes perpendicular to the horizontal surface, as shown in part (b). A unifrom magnetic field B, constant in time and is directed upwards, perpendicular to the horizontal surface. The field completely fills the region occupied by the coil in either part of the drawing. The magnitude of the magnetic field is `B = 2 T`.
(a)
The resistance of the coil is `0.4 Omega`, and the smaller semicircle has a radius of `20 cm`. while the bigger one has a radius of `40 cm`. The angular frequency at which the small semicircle rotates is `omega = 15 rad//s`. Determine the average current I, if any, induced in the coil as the coil changes shape from that in part (a) of the drawing to that in part (b)

Options

A. `0 A`
B. `1 A`
C. `2 A`
D. `3 A`

Answer

D

Explanation

The change inn flux `Delta phi = (pi)/(2)r^(2)B`, where `r = 0.2 m`
Average emf `= (Delta phi)/(pi//2 omega)`
Current `=` averaged emf / resistance