I was not able to derive the charge on the capacitor. But then, I arbitrarily assumed ##\phi=B.A## (Dot product of Magnetic field and Area)
Then, proceeding as follows,
##\phi=BA\cos(\omega_0 t)##
##\frac{d\phi}{dt}=−BA\omega_0\sin(\omega_0 t)##
Now at ##t=0, \phi=BA\cos(0)=BA##
Therefore...