A fully charged capacitor $$C$$ with initial charge $${q_0}$$ is connected to a coil of self inductance $$L$$ at $$t = 0.$$  The time at which the energy is stored equally between the electric and the magnetic fields is:

Solution :
Energy stored in magnetic field = $$\frac{1}{2}L{i^2}$$
Energy stored in electric field = $$\frac{1}{2}\frac{{{q^2}}}{C}$$
$$\eqalign{ & \therefore \frac{1}{2}L{i^2} = \frac{1}{2}\frac{{{q^2}}}{C} \cr & {\text{Also }}q = {q_0}\cos \omega t{\text{ and }}\omega = \frac{1}{{\sqrt {LC} }} \cr} $$
On solving $$t = \frac{\pi }{4}\sqrt {LC} $$