Answer
The charge on the capacitor is $~~0.577~Q$
Work Step by Step
If the energy stored in the electric field is 50.0% of the energy stored in the magnetic field, then the electric field stores $\frac{1}{3}$ of the total energy and the magnetic field stores $\frac{2}{3}$ of the total energy at that moment.
We can find the charge $q$ on the capacitor at that moment:
$\frac{q^2}{2C} = \frac{1}{3}~\frac{Q^2}{2C}$
$q^2 = \frac{Q^2}{3}$
$q = \sqrt{\frac{1}{3}}~Q$
$q = 0.577~Q$
The charge on the capacitor is $~~0.577~Q$
