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(A) The total energy in an oscillating $LC$ circuit is constant and is given by the maximum energy stored in the capacitor: $U_{total} = \frac{Q^2}{2C

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

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(A) The total energy in an oscillating $LC$ circuit is constant and is given by the maximum energy stored in the capacitor: $U_{total} = \frac{Q^2}{2C}$.When the energy is shared equally between the electric field $(U_E)$ and the magnetic field $(U_B)$, we have $U_E = U_B = \frac{1}{2} U_{total}$.The energy stored in the capacitor at any instant with charge $q$ is $U_E = \frac{q^2}{2C}$.Setting this equal to half the total energy: $\frac{q^2}{2C} = \frac{1}{2} \left( \frac{Q^2}{2C} \right)$.Simplifying the equation: $q^2 = \frac{Q^2}{2}$.Taking the square root of both sides: $q = \frac{Q}{\sqrt{2}}$.

In an oscillating $LC$ circuit, the maximum charge on the capacitor is $Q$. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

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