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

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Aicharya · Accepted Answer

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

In an oscillating \(L C\) circuit, the maximum charge on the capacitor is \(Q\). The charge on the capacitor…

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