Energy stored in a magnetic field:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{L}}{{\mathbf{i}}}^{{\mathbf{2}}}}$

Energy stored in a capacitor:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{Q}\mathbf{V}}{\mathbf{2}}{\mathbf{=}}\frac{\mathbf{C}{\mathbf{V}}^{\mathbf{2}}}{\mathbf{2}}{\mathbf{=}}\frac{{\mathbf{Q}}^{\mathbf{2}}}{\mathbf{2}\mathbf{C}}}$

Consider an L-C circuit with capacitance C, inductance L, and no voltage source, as shown in the figure (Figure 1). As a function of time, the charge on the capacitor is Q(t) and the current through the inductor is I(t). Assume that the circuit has no resistance and that at one time the capacitor was charged.

Part A. As a function of time, what is the energy U_{L}(t) stored in the inductor?

Express your answer in terms of L and I(t).

U_{L}(t) =

Part B. As a function of time, what is the energy U_{C}(t) stored in the inductor? Express your answer in terms of C and Q(t).

U_{C}(t) =

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