Electric charge

Electric charge can be directly measured with an electrometer. Its unit is the coulomb. Observed particles have charges which are positive or negative integer multiples of the elementary charge which is a fundamental physical constant. The discrete nature of electric charge was demonstrated by Robert Millikan in his oil-drop experiment.

Most physicists believe that hadrons contain quarks which have charges which are multiples of one-third the elementary charge, but cannot be observed except in combinations which have charge that is a multiple of the elementary charge.

History

Charge was discovered by the Ancient Greeks who found that rubbing fur on various substances, such as amber, would build up an electric charge imbalance. The Greeks noted that the charged amber buttons could attract light objects such as hair. The Greeks also noted that if they rubbed the amber for long enough, they could even get a spark to jump. The word electricity derives from ηλεκτρον, the Greek word for amber.

By the 18th century, the study of electricity had become popular. One of the foremost experts was a man named Benjamin Franklin. Franklin imagined electricity as being a type of invisible fluid present in all matter. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with the type of charge acquired by a glass rod rubbed with silk, and "negative" with that acquired by an amber rod rubbed with fur.

We now know that Franklin's model was too simple. Matter is actually composed of two kinds of electricity: particles called protons which carry a charge of positive electricity, and particles called electrons which carry a charge of negative electricity. Rather than one possible electric current there are many: a flow of negative particles, or a flow of positive particles, or a flow of both negative and positive particles in opposite directions. To reduce this complexity, electrical workers still use Franklin's convention and they imagine that electric current (known as conventional current) is a flow of exclusively positive particles. The conventional current simplifes electrical concepts and calculations, but it ignores the fact that within some conductors (electrolytes, semiconductors, and plasma,) two or more species of electric charges flow in opposite directions. The flow direction for Conventional Current is also backwards compared to the actual electron drift taking place during electric currents in metals.

Properties

Aside from the properties described in articles about electromagnetism, it is worth noting that charge is a relativistic invariant. What this means is that any particle that has charge q, no matter how fast it goes, always has charge q. This property has been experimentally verified by showing that the charge of a helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at incredible speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).

Conservation of Charge and Gauge invariance

plus other terms that do not involve the electromagnetic interaction. since the contribution to the action by the first term is trivially gauge invariant, we need consider only the second. Under a gauge transformation A_i->A_i+∂_iφ the action is increased by

the only way for this to be satisfied for arbitary φ is if ∂_μJ^μ=0, which is the continuity equation

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