Energy Stored in Magnetic Field In an oscillating L C...

Energy Stored in Magnetic Field In an oscillating $L C$ circuit, $75.0 \%$ of the total energy is stored in the magnetic field of the inductor at a certain instant. (a) In terms of the maximum charge on the capacitor, what is the charge there at that instant? (b) In terms of the maximum current in the inductor, what is the current there at that instant?

Key Concepts

LC Circuit Oscillations

An LC circuit is a classic oscillator where energy continuously exchanges between an electric field (in the capacitor) and a magnetic field (in the inductor). This oscillation is governed by the interplay of the circuit's capacitance (C) and inductance (L), resulting in periodic variations in voltage and current.

Energy Stored in Capacitor

The energy stored in a capacitor is given by the expression U_C = ½ Q²/C, where Q is the instantaneous charge. This quantity represents the potential energy arising from the separation of charge across the capacitor's plates, and it reaches a maximum when the capacitor is fully charged.

Energy Stored in Inductor

The energy stored in the magnetic field of an inductor is expressed as U_L = ½ L i², where i is the instantaneous current. This energy is associated with the magnetic field created by the flow of current through the inductor, and it is maximized when the current is at its peak.

Conservation of Energy

In an ideal LC circuit with no resistive losses, the total energy remains constant over time. This conservation of energy principle ensures that any decrease in energy stored in one component (capacitor or inductor) is exactly balanced by an increase in the other, enabling the oscillatory behavior of the circuit.

Maximum Charge and Maximum Current

The concepts of maximum charge (Q_max) and maximum current (I_max) refer to the extremal conditions of the LC circuit's energy states. At the points of maximum charge, the stored energy is entirely in the capacitor, while at maximum current, all energy is in the magnetic field of the inductor. These maximum values serve as benchmarks for analyzing the instantaneous energy distribution within the circuit.

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