1. Electromagnetic Oscillations

Concept Explanation:
Electromagnetic oscillations refer to the periodic variations in the electric and magnetic fields within a circuit or system. These oscillations are commonly produced in LC circuits, which consist of an inductor (L) and a capacitor (C). The energy in an LC circuit oscillates between the electric field of the capacitor and the magnetic field of the inductor.

Working Principle:
- When a charged capacitor is connected to an inductor, the capacitor begins to discharge, creating a current through the inductor.
- The current generates a magnetic field around the inductor, storing energy in the magnetic field.
- As the capacitor discharges, its voltage decreases until it is fully discharged, at which point the magnetic field collapses, inducing a current in the opposite direction.
- This process repeats, creating oscillating currents and voltages in the circuit.

Mathematical Representation:
The natural frequency of oscillation ω₀ in an LC circuit is given by:
ω₀ = 1/√(LC)

The oscillations can be described by the equations:
q(t) = Q cos(ω₀t + φ)
i(t) = -ω₀Q sin(ω₀t + φ)
where:
- q(t) is the charge on the capacitor at time t,
- i(t) is the current through the inductor at time t,
- Q is the maximum charge, and
- φ is the phase angle.

Example Problem:
An LC circuit has an inductance of 2 mH and a capacitance of 10 μF. Calculate the natural frequency of oscillation.

Solution:
Using the formula for the natural frequency:
ω₀ = 1/√(LC) = 1/√(2 × 10⁻³ × 10 × 10⁻⁶) = 1/√(2 × 10⁻⁸) = 7.07 × 10³ rad/s
The natural frequency of oscillation is approximately 7.07 kHz.