In the figure `ABCDEFA` is closed conducting wire loop. The part `AFE` is a portion of an ellipse, `(X^(2))/(4a^(2))+(Y^(2))/(a^(2))=1` and `BCD` is a portion of the ellipse `(X^(2))/(9a^(2))+(Y^(2))/(4a^(2))=1`
`A` uniform magnetic field
`vecB=B_(0)hatk` exists in this region. If the frame is rotated about the `y-` axis with a constant angulat velocity `'omega'`. Find the maximum emf induced in the loop.

Explanation

`a_(1)=2a` `b_(1)=a`
`a_(2)=3a` `b_(2)=2a`
Area of wire frame
`(pi[a_(2)b_(2)-a_(1)b_(1)])/(2)=2pia^(2)`
`phi=2piB_(0)a^(2)cos(omegat)`
`epsilon=-(dphi)/(dt)=2piomegaB_(0)a^(2)sin(omegat)`
peak emf `=2piomegaB_(0)a^(2)`