A wire bent as a parabola `y=ax^(2)` is located in a uniformed magnetic field of induaction `B` , the vector `B` being perpendicular to the plane `x-y` . At moment `t=0` a connector starts sliding translationwise from the parabola apex with a constant acceleration `omega` . Find the emf of electromagnetic induction in the loop thus formed as a function of `y`

Explanation

`y=(1)/(2)omegat^(2)implies t=sqrt((2y)/(omega))`
`y=ax^(2) implies x=sqrt((y)/(a))`
Length of rod `t=2x=2sqrt((y)/(a))`
`v=omegat=omegasqrt((2y)/(omega))=sqrt(2omegay)`
`e=Bvl=Bsqrt(2omegay).2sqrt((y)/(a))`
`=Bysqrt((8omega)/(a))`