This question is an exact duplicate of:
See as per the question, The Inductor pretty much will induce emf due to magnetic field and not due to other coil/current nearby. Thus I used $E= - d(phi(t))/dt$ as the induced emf.
Then using (magnitude of q=CV) I put V=E thus getting q(t)=C . d(phi(t))/dt
Also I took phi(t) = B.A.coswt arbitrarily where at t=0, phi = B.A And so I got the 2nd option. Please help me. Is my solution correct? Also can you help with 4th option? I presume its not related to the question at all?
Edit:- Sorry with my Latex. I dont know how to write it properly.