Free electromagnetic oscillations (the oscillating circuit). Energy changes in the circuit
A closed circuit of a capacitor (C) and an inductive coil (L) is called an oscillating circuit. A charged capacitor discharges through the coil: because of self-induction the current rises slowly and the electric field energy q²/(2C) turns into the magnetic field energy Li²/2 of the coil; when the capacitor is fully discharged the current is greatest and the charge is zero. Then the coil's current, maintained by self-induction, recharges the capacitor with the opposite sign and the process repeats: these are free electromagnetic oscillations. In an ideal circuit of zero active resistance the total energy does not change: W = q²/(2C) + Li²/2 = qₘ²/(2C) = LIₘ²/2. The period is given by Thomson's formula T = 2π√(LC), and the frequency ν = 1/T = 1/(2π√(LC)); if L or C increases, the period increases. The mechanical analogy: q is the coordinate, i the velocity, L the mass and 1/C the stiffness.
Make a table in your notebook for a spring pendulum and an oscillating circuit: coordinate – charge, velocity – current, mass – inductance, stiffness – 1/C. For each quarter of the period mark when the «energy» is entirely potential (electric) and when entirely kinetic (magnetic).