In an oscillating LC circuit, the maximum charge on the capacitor...

Total energy of the LC circuit is given by the maximum energy stored in the capacitor:

$U_{total} = \dfrac{Q^2}{2C}$

When the energy is stored equally between the electric and magnetic fields, the electric energy $U_E$ is half of the total energy:

$U_E = \dfrac{1}{2} U_{total}$

The electric energy at this instant is given by:

$U_E = \dfrac{q^2}{2C}$

Equating the expressions for $U_E$:

$\dfrac{q^2}{2C} = \dfrac{1}{2}$\left( \dfrac{Q^2}{2C} \right)

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

$Q =$\sqrt{2}$q$

Answer: $Q =$\sqrt{2}\, q