In an ideal LC circuit, if the energy stored in the inductor is...

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$):<br><br>$E_{total} = 2U_C$<br><br>Substituting the expressions for energy:<br><br>\dfrac{Q_0^2}{2C} = 2$\left( \dfrac{Q^2}{2C} \right)

$Q^2 =$\dfrac{Q_0^2}{2}$<br><br>$Q = \dfrac{Q_0}{\sqrt{2}}$<br><br>Answer:$\dfrac{Q_0}{\sqrt{2}}