A wire loop enclosing a semi-circle of radius `a=2cm` is located on the boundary of a uniform magnetic field of induction `B=1T` (figure).At the moment `t=0` the loop is set into rotation with a constant angular acceleration `beta=2 rad//sec^(2)` about an axis `O` coinciding with a line of vector `B` on the boundary.The `emf` induced in the loop as a function of time `t` is `[x xx10^(-4)(-1)^(n)xxt]V`, where `n=1,2,...` is the number of the half-revolution taht the loop performs at the given moment `t`.Find the value of `x`.(The arrow in the figure shows the `emf` direction taken to be positive, at `t=0` loop was completely outside)

Answer

D

Explanation

Flux=`phi=vecA.vecB=-(a^(2)/2theta)B rArrphi=-a^(2)/2((betat^(2))/2)B rArre=-(domega)/(dt)=(a^(2)Bbetat)/2(-1)^(n)`