Electric Charge and Electric Current

Electric charge is the property that makes a particle feel and exert an electric force; an electric current is charge in motion — and it is that motion, not the charge itself, that produces a magnetic field. The international system of units defines the second of those in terms of the first.

One particle, one counting unit

NIST calls the charge on an electron the elementary charge e; in an atom, the proton carries exactly that magnitude with the opposite sign.

The unit of charge is the coulomb (C). Since 20 May 2019, e = 1.602176634 × 10⁻¹⁹ C, and NIST's CODATA 2022 table gives its standard uncertainty as "(exact)" — exact by definition. One coulomb therefore holds about 6.241 × 10¹⁸ elementary charges.

The ampere: from a force between two wires to a constant

The old definition of the ampere was a mechanical statement: two "straight parallel conductors of infinite length" placed 1 metre apart in vacuum would "produce between these conductors a force equal to 2 x 10⁻⁷ newton per meter of length" (NIST). It broke in two ways: nobody has infinitely long wires, so the ampere could not be realised according to its own definition; and it described an electrical unit in the language of force, which tied it to the standard of mass.

BIPM's current definition reverses that dependency: the ampere "is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 x 10⁻¹⁹ when expressed in the unit C, which is equal to A s". One ampere is therefore a current carrying one coulomb past a point in one second, and both sides are anchored to constants: charge to e, time to the frequency of the caesium transition.

The Kibble balance offsets the weight of a test mass with the force produced by running a current through a coil sitting in a magnetic field, then derives mass from measurements of current and voltage (NIST). The ampere once had to borrow the kilogram in order to define itself; now the kilogram is realised by an electrical measurement.

Conventional direction is not the electrons' direction

Current is conventionally taken to flow from higher potential to lower potential, that is, along the direction positive charge would move. But in a metal wire the real carriers are electrons, and they travel the other way: the convention was fixed before anyone knew electrons existed, and as Engineering LibreTexts puts it bluntly, "Franklin guessed wrong."

Current that needs no copper wire

According to the US National Weather Service, "a typical lightning flash is about 300 million Volts and about 30,000 Amps", against a US household current of "120 Volts and 15 Amps"; lightning is the moment when "this insulating capacity of the air breaks down". Solar storms, for their part, "accelerate charged particles — electrons and protons — into space at incredibly high speeds" (NASA), and it is that stream of particles, falling into the two polar regions, that produces the aurora. The human body runs on ionic currents, and the sign convention above still holds: in the textbook Neuroscience, an inward current means "a positive charge entering the cell—that is, cations in or anions out", and "a transient increase in the permeability of the neuronal membrane to Na+ initiates the action potential" — the membrane current Hodgkin and Huxley described quantitatively in 1952.