Problem 4.100

An oscillating circuit consists of an inductance coil $L$ and a capacitor with capacitance $C .$ The resistance of the coil and the lead wires is negligible. The coil is placed in a permanent magnetic field so that the total flux passing through all the turns of the coil is equa] to \Phi. At the moment $t=0$ the magnetic field was switched off. Assuming the switching off time to be negligible compared to the natural oscillation period of the circuit, find the circuit current as a function of time $t$.