LC oscillating circuit — wave emission

What just happened?

In an LC circuit the charge sloshes round and round: the capacitor discharges through the inductor, and the inductor — thanks to induction — charges the capacitor back up, but with the opposite sign. Electrical oscillations arise. A connected antenna turns them into an electromagnetic wave sent out into space — this is how a radio wave is born.

Oscillation frequency (Thomson’s formula):

— the smaller the product $L\cdot C$, the higher the frequency $f$, and so the shorter the wave ($\lambda = c/f$). L — inductance of the coil (H), C — capacitance of the capacitor (F), f — frequency (Hz).

Conservation of energy:

In an ideal circuit (no resistance) the total energy is constant — it only sloshes between the electric field of the capacitor and the magnetic field of the inductor:

Analogy with a pendulum:

The LC circuit oscillates like a pendulum. The capacitor plays the role of the spring (it stores potential energy — field E), and the inductor the role of the mass (it stores energy of motion — field B). The energy is now "in the spring", now "in the motion", and its total does not change — exactly as in mechanical oscillations.

Why you need this for the exam:

The formula $f = 1/(2\pi\sqrt{LC})$ plus $\lambda = c/f$ solve most problems about oscillating circuits and radio waves. The trick: compute f from Thomson’s formula, then the wavelength from the speed of light.

Remember: an LC circuit oscillates faster the smaller the product L·C, and the total energy circulates between field E and field B and never disappears — f = 1/(2π√(LC)).