Italy Secondaria di secondo grado – classe 5ª (esame di Stato) Physics (other licei)

1. Electromagnetism

Electric and magnetic fields · Induction and EM waves · 20th-century physics (recommended)

• Electric Charges and Fields – Charge comes in two kinds, is conserved and comes in whole-number packets of e = 1.6 × 10⁻¹⁹ C. Two point charges push or pull with F = kq₁q₂/r² (k = 9 × 10⁹ N m² C⁻²). Forces and fields from many charges add as vectors (superposition). The field E = F/q₀ of a point charge is kq/r²; field lines show it. A dipole (±q a distance 2a apart) has moment p = q·2a; in a uniform field it feels zero net force but a torque τ = pE sinθ. Electric flux Φ = E·A, and Gauss's law says the flux out of any closed surface is q_enclosed/ε₀, which quickly gives E for a long wire (λ/2πε₀r), a plane sheet (σ/2ε₀) and a thin spherical shell (kq/r² outside, 0 inside).
• Electromagnetic Induction – When the magnetic flux through a coil changes, an emf is produced in it: ε = −N dΦ/dt (Faraday). The minus sign is Lenz's law: the induced current always opposes the change that made it. Moving a rod in a field gives motional emf ε = Blv. A changing current makes an emf in its own coil (self-induction, L) and in a nearby coil (mutual induction, M).
• Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.
• Modern Physics: Quantum Theory and Relativity – Modern physics began around 1900, when classical physics failed for the very small and the very fast. Quantum theory says energy comes in packets: a photon has E = hf. The photoelectric effect shows light acts as particles, while interference shows particles such as electrons act as waves (λ = h/p). Special relativity says the speed of light is the same for all observers, so moving clocks run slow (t = γt₀), moving lengths shrink, and mass is energy (E = mc²). These ideas power lasers, solar cells, electron microscopes, GPS and nuclear energy.