Electricity is movement of charge carriers (electrons/ions) through a conductor (in the body through conductive fluid and tissue) and requires direct contact (electrodes) and it works by moving ions.
Electric and magnetic fields coupled together is called electromagnetism. A changing electric field creates a magnetic field and vice versa. When they detach and travel through space, you get an electromagnetic wave (radio, microwave, infrared, light, THz, etc.) where no contact is needed, it's radiating.
Electricity (DC) needs electrodes on the skin for transfer. Depolarizes nerve- and muscle membranes which triggers action potentials. A muscle contracts, pain signals are blocked. An ionic mechanism and forcing Na⁺/K⁺/Ca²⁺ across (cell)membranes. The effect is local and occurs where current flows.
Static magnetic field pass through tissue freely. Human tissue is essentially non-magnetic, so a static field has almost no meaningful biological effect.
Pulsed electromagnetic field (PEMF) A changing magnetic field induces tiny electric currents inside tissue (Faraday's law) — without electrodes. These induced micro-currents can affect ion channels and membrane potential. The depth depends on field strength and frequency.
Electromagnetic waves (the radiation spectrum) Here frequency decides everything, because frequency is photon energy. Radio or microwave are non-ionizing when low frequencies are used and its main effect is thermal. Water is heated and tissue gets penetrated deeper with low frequencies. High frequencies such as UV/x-ray/ gamma are damaging (cell)tissue. Thez are ionizing enough photon energy to break bonds and damage DNA.
Terahertz is non-ionizing, absorbed by water in the top skin layers. It barely penetrates and is used mostly for surface heating.
Infrared / red light is absorbed by tissue chromophores. Red /near-IR can influence mitochondria and is called photobiomodulation. It reaches a shallow depth.
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