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(C) The total energy in an $L-C$ circuit is constant and is given by $U = U_E + U_B$,where $U_E = \frac{q^2}{2C}$ is the electric energy and $U_B = \f

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$Q/\sqrt{2}$

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(C) The total energy in an $L-C$ circuit is constant and is given by $U = U_E + U_B$,where $U_E = \frac{q^2}{2C}$ is the electric energy and $U_B = \frac{1}{2}Li^2$ is the magnetic energy.At maximum charge $Q$,the current $i = 0$,so the total energy is $U = \frac{Q^2}{2C}$.When the energy is stored equally between the electric and magnetic fields,we have $U_E = U_B$.Since $U = U_E + U_B$,it follows that $U_E = \frac{1}{2}U$.Substituting the expressions for energy:$\frac{q^2}{2C} = \frac{1}{2} \left( \frac{Q^2}{2C} \right)$$\frac{q^2}{2C} = \frac{Q^2}{4C}$$q^2 = \frac{Q^2}{2}$$q = \frac{Q}{\sqrt{2}}$

In an oscillating $L-C$ 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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