Properties of Electric Charges

Electric charge is a fundamental physical property of matter that has many parallels to mass.

Learning Objective

Describe properties of electric charge, such as its relativistic invariance and its conservation in closed systems

Key Points

Charge is measured in Coulombs (C), which represent 6.242×10¹⁸ e, where e is the charge of a proton. Charges can be positive or negative, and as such a singular proton has a charge of 1.602×10⁻¹⁹ C, while an electron has a charge of -1.602×10⁻¹⁹ C.
Electric charge, like mass, is conserved. The force generated by two charges is of the same form as that generated by two masses and, like gravity, force from an electrical field is both conservative and central.
Electric charge is a relativistic invariant. That is, charge (unlike mass) is independent of speed. Whereas the mass of a particle will exponentially rise as its speed approaches that of light, charge will remain constant.

Terms

gravity
Resultant force on Earth's surface, of the attraction by the Earth's masses, and the centrifugal pseudo-force caused by the Earth's rotation.
coulomb
In the International System of Units, the derived unit of electric charge; the amount of electric charge carried by a current of 1 ampere flowing for 1 second. Symbol: C
electric field
A region of space around a charged particle, or between two voltages; it exerts a force on charged objects in its vicinity.

Full Text

Properties of Electric Charge

Electric charge, like mass and volume, is a physical property of matter. Its SI unit is known as the Coulomb (C), which represents 6.242×10¹⁸e, where e is the charge of a proton. Charges can be positive or negative; a singular proton has a charge of 1.602×10⁻¹⁹ C, while an electron has a charge of -1.602×10⁻¹⁹ C.

Invariance

Like mass, electric charge in a closed system is conserved. As long as a system is impermeable, the amount of charge inside it will neither increase nor decrease; it can only be transferred. However, electric charge differs from other properties—like mass—in that it is a relativistic invariant. That is, charge is independent of speed. The mass of a particle will rise exponentially as its speed approaches that of light, its charge, however, will remain constant.

The independence of electric charge from speed was proven through an experiment in which one fast-moving helium nucleus (two protons and two neutrons bound together) was proven to have the same charge as two separate, slow-moving deuterium nuclei (one proton and one neutron bound together in each nucleus).

Attraction and Repulsion

Electric charge is a property that produces forces that can attract or repel matter. Mass is similar, although it can only attract matter, not repel it. Still, the formula describing the interactions between charges is remarkably similar to that which characterizes the interactions between masses. For electric fields, the force (F) is related to the charges (q₁, q₂) and the distance (r) between them as:

$F=\frac{1}{4\pi \epsilon_0}\frac {q_1q_2}{r^2}$

where π and $\epsilon_0$ are constants. This is known as Coulomb's Law.

Coulomb's Law

The forces (F₁ and F₂) sum to produce the total force, which is calculated by Coulomb's Law and is proportional to the product of the charges q₁ and q₂, and inversely proportional to the square of the distance (r₂₁) between them.

The formula for gravitational force has exactly the same form as Coulomb's Law, but relates the product of two masses (rather than the charges) and uses a different constant. Both act in a vacuum and are central (depend only on distance between the forces) and conservative (independent of path taken). However, it should be noted that when comparing similar terms, charge-based interaction is substantially greater than that based on mass. For example, the electric repulsion between two electrons is about 10⁴² times stronger than their gravitational attraction.

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