In an oscillating \(L C\) circuit, the maximum charge on the capacitor is \(Q\). The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is

Given, in an oscillating \(L C\) circuit, maximum charge on the capacitor \(=Q\) We know that, total energy stored in the capacitor, \(U=\frac{1}{2} \frac{Q^2}{C}\) \(\therefore\) Energy is equally distributed in a electric field and magnetic field, so the energy stored in the capacitor is half of maximum. \(\therefore \frac{1}{2}\) (energy stored in \(C\), in electric field) \(=\) energy stored in \(C\), in magnetic field \(\begin{array}{rlrl} \therefore & \frac{1}{2} \times \frac{1}{2} \frac{Q^2}{C} =\frac{1}{2} \times \frac{Q^{\prime 2}}{C} \\ \text { or } & \frac{1}{4} \frac{Q^2}{C} =\frac{1}{2} \times \frac{Q^{\prime 2}}{C} \\ \text { or } & Q^{\prime 2} =\frac{2 Q^2}{4} \\ \text { or } & Q^{\prime} =\frac{Q}{\sqrt{2}} \end{array}\) Hence, the charge on the capacitor when the energy is started equally between the electric and magnetic field is \(\frac{Q}{\sqrt{2}}\).