Foundation · Explanatory preview
Forces on charges, currents, and electromagnetic waves
Electric charges produce electric fields and experience forces q E; moving charges experience magnetic forces q v x B. Bound charges act as resonators absorbing and emitting electromagnetic waves at the speed of light.
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How do charges interact with electric and magnetic fields?
Electric charge is the intrinsic property of matter that produces and responds to electromagnetic fields. A charge q at rest in an electric field E experiences an electrostatic force F = q E. When moving with velocity v through a magnetic field B, the charge experiences an additional perpendicular magnetic force F = q (v x B). Together, these form the Lorentz force.
Moving a charge through an electric potential difference Delta V transfers potential energy Delta W = q Delta V. For a fundamental electron charge e = 1.602e-19 C accelerated across a potential of 1 V, the energy gained is defined as 1 electron-volt (1 eV = 1.602e-19 J).
In microscopic matter, an electron bound to an equilibrium position by a restoring force acts as a harmonic oscillator or resonator. When disturbed by incoming electromagnetic waves, it absorbs and reradiates energy at its natural resonant frequency nu_0. Einstein's 1905 light-quanta paper opened with Planck's model of such resonators in thermal equilibrium with radiant energy.
Maxwell's electrodynamics expresses four physical laws in words: electric charges act as sources of electric flux; magnetic field lines are closed loops with no isolated magnetic charges; a time-varying magnetic field induces a circulating electric field (Faraday induction); and electric currents alongside time-varying electric fields generate circulating magnetic fields (Maxwell-Ampere law). Combined, these equations govern self-propagating electromagnetic waves traveling at speed c in vacuum.
Einstein pointed out in 1905 that classical electrodynamics treated the relative motion of a magnet and a conductor with an artificial asymmetry: moving the magnet created an electric field in space that drove current, whereas moving the conductor created no electric field but rather a magnetic Lorentz force on electrons. Yet the physical current was identical in both descriptions.
One worked example
Force equals charge times the sum of electric field and the cross product of velocity with magnetic field, and work equals charge times potential difference.
Accelerating an electron of charge e = 1.602e-19 Coulombs across an electric potential difference of Delta V = 1.0 Volt gives kinetic energy Delta W = (1.602e-19 C)(1.0 V) = 1.602e-19 Joules = 1 eV. An electron bound with effective spring constant k_s and mass m oscillates at natural frequency nu_0 = (1 / 2 pi) sqrt(k_s / m).
A stopping point: Charge is the property that makes electric forces; fields mediate force between separated charges without action-at-a-distance.
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