Electric force depends on charge and distance {Coulomb's law} {Coulomb law}. Electric force F between two charges varies directly with charge q and varies inversely with square of distance r between charges: F = k * q1 * q2 / r^2 = (1 / (4 * pi * e)) * q1 * q2 / r^2.
permittivity
Electric-force constant k depends on medium electric permittivity e: k = 1 / (4 * pi * e).
distance
Force varies with distance squared, because space is isotropic in all directions, time has no effect, and field-line number stays constant as surface area increases. Sphere surface area = 4 * pi * r^2.
charge
Force depends on both charges, because force is interaction. Electric force depends on charge linearly, because charge directly causes force. Because charges can be positive or negative, electric force can be attractive positive or repulsive negative. If both charges are positive or negative, electric force is positive. If one charge is positive and one charge is negative, electric force is negative.
comparison
Electric force is very strong compared to gravity. Gravitational force and electric force equations are similar, because interactions cause both forces and both forces radiate in all directions.
voltage
dW = F * ds = q * dV. F = q * dV / ds = q * E.
In potential equations {d'Alembert equation, electromagnetism} for electric and magnetic fields, source-charge density and three current-density components make four potentials for each field.
For stationary magnet and moving wire in a circuit, electric force F makes electric current, and force varies directly with magnetic-flux (phi, depending on magnetic field B and surface area A) change over time {Faraday law of induction} {Faraday's law of induction}: F ~ d(phi)/dt, and phi = sum over A of B. Induced electric current makes magnetic field opposed to stationary magnetic field. For moving magnet and stationary wire, electric field E makes electric current in wire, and electromotive force on charges varies directly with magnetic-flux change over time. Faraday law of induction applies to both Maxwell-Faraday equation, for changing magnetic field and stationary charge, and Lorentz force law, for stationary magnet and moving wire in a circuit.
A constant {fine-structure constant} {coupling constant} measures electromagnetism force strength (Sommerfield) [1916]. It has no dimensions. It equals 7.297 * 10^-3 ~ 1/137. The fine-structure constant depends on electron charge, Planck constant, light speed, and permittivity or permeability or Coulomb constant. The coupling constant measures photon-electron force.
For changing magnetic field and stationary charge, changing magnetic field B makes electric field E {Maxwell-Faraday equation} {Faraday's law}: curl of E = partial derivative over time of B. This has an integral form {Kelvin-Stokes theorem}: line integral of E = integral over surface area of partial derivative of B with time.
For stationary magnet and moving wire in a circuit, Lorentz force F on charges makes electric current and electric force varies directly with electric charge q and with wire velocity v and magnetic field B cross product {Lorentz force law}: F ~ q * (v x B). Induced electric current makes magnetic field opposed to stationary magnetic field.
Flux equals integral of electric field E over area A, which equals sum of charges q divided by electric permittivity e {Gauss' law} {Gauss law}: integral of E * dA = (sum of q) / e. Gauss' law can find electric field and voltage.
Divergence of magnetic field B equals zero {Gauss law of magnetism} {Gauss's law of magnetism} {transversality requirement} {absence of free magnetic poles}: divergence of B = 0, or line integral over a surface of B = 0. Magnetic fields are solenoids. Magnetic "charges" are dipoles, and there are no magnetic monopoles.
Electric fields are like force lines {force lines} {lines of force}| radiating from center outward in all directions. Force lines per area equal electric field. Force lines have direction, from positive to negative, because test charges are positive. Force lines entering closed surfaces are negative. Force lines leaving closed surfaces are positive. For large charged objects, electric-field lines are perpendicular to surfaces, because force lines are symmetric around surface perpendiculars.
Electric-force lines pass through areas in directions {flux, electric} {electric flux}. Positive and negative fluxes from different sources add together. Does infinite flux exist? Perhaps, field lines cannot come closer than Planck length. Then flux has maximum density, and field has no infinities.
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Date Modified: 2022.0225