Final answer:
The maximum energy stored in the inductor of an LC circuit is calculated using the formula U_L = ½ LI². Since the maximum energy stored in the inductor equals the initial energy stored in the capacitor, we use the initial conditions provided to find the peak current and the maximum energy in the inductor.
Step-by-step explanation:
The question asks for the maximum energy stored in the inductor of an L-C circuit with an inductor of 60.0 mH and a capacitor of 290 μF, where the initial charge on the capacitor is 6.00 μC and the initial current in the inductor is 0.500 mA. To find the maximum energy stored in the inductor, we can use the energy formula for inductors, UL = ½ LI², where L is the inductance and I is the current.
However, in this case, we're given the initial current, but we need to determine the peak current to find the maximum energy. The initial energy stored in the capacitor can be calculated using UC = ½ Cq². Because energy in an ideal LC circuit is conserved and oscillates between the capacitor and inductor, the maximum energy stored in the inductor will equal the initial energy stored in the capacitor.
So first, we calculate the initial energy stored in the capacitor:
½ × (290 × 10-6 F) × (6.00 × 10-6 C)2 = UC
Then, since UL = UC at maximum energy, we equate this to the formula for inductor energy to solve for the peak current and subsequently, for the maximum energy in the inductor.