In an ideal LC circuit, if the energy stored in the inductor is equal to energy stored in a capacitor, then the magnitude of charge Q stored in capacitor is ( $Q_0$ is the maximum charge)

Total energy in an ideal LC circuit is conserved and is equal to the maximum energy stored in the capacitor.

$E_{total} = \dfrac{Q_0^2}{2C}$

At any instant, the total energy is the sum of the energy stored in the capacitor ($U_C$) and the inductor ($U_L$).

$E_{total} = U_C + U_L$

Given that the energy stored in the inductor is equal to the energy stored in the capacitor ($U_L = U_C$):

$E_{total} = 2U_C$

Substituting the expressions for energy:

$\dfrac{Q_0^2}{2C} = 2 \left( \dfrac{Q^2}{2C} \right)$

$Q^2 = \dfrac{Q_0^2}{2}$

$Q = \dfrac{Q_0}{\sqrt{2}}$

Answer: $\dfrac{Q_0}{\sqrt{2}}$