In an oscillating LC circuit,the maximum char | vedclass

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

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$Q/\sqrt{2}$

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(C) The total energy $U_{T}$ in an oscillating $LC$ circuit is constant and is given by the maximum energy stored in the capacitor: $U_{T} = \frac{Q^{2}}{2C}$.When the energy is stored equally between the electric field (capacitor) and the magnetic field (inductor),the energy in the capacitor $U_{E}$ is half of the total energy: $U_{E} = \frac{U_{T}}{2}$.Substituting the expressions for energy,we get: $\frac{q^{2}}{2C} = \frac{1}{2} \left( \frac{Q^{2}}{2C} \right)$.Simplifying this,we have: $q^{2} = \frac{Q^{2}}{2}$.Taking the square root of both sides,the charge on the capacitor is $q = \frac{Q}{\sqrt{2}}$.

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

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