Physics - Capacitor Question with Solution | TestHub

The total energy of the oscillating LC circuit is given by $U=\frac{Q^2}{2C}$

Let $q$ be the charge on the capacitor when the energy is equally shared between the electric and magnetic fields.

The electric energy stored in the capacitor at this instant is $U_E=\frac{q^2}{2C}$

Since the energy is equally divided between the electric and magnetic fields, the electric energy is half of the total energy:

$U_E=\frac{U}{2}$

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

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

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

Answer: $\frac{Q}{\sqrt{2}}$