# 28.1 Static electricity and charge: conservation of charge  (Page 4/8)

 Page 4 / 8

No charge is actually created or destroyed when charges are separated as we have been discussing. Rather, existing charges are moved about. In fact, in all situations the total amount of charge is always constant. This universally obeyed law of nature is called the law of conservation of charge    .

## Law of conservation of charge

Total charge is constant in any process.

In more exotic situations, such as in particle accelerators, mass, $\Delta m$ , can be created from energy in the amount $\Delta m=\frac{E}{{c}^{2}}$ . Sometimes, the created mass is charged, such as when an electron is created. Whenever a charged particle is created, another having an opposite charge is always created along with it, so that the total charge created is zero. Usually, the two particles are “matter-antimatter” counterparts. For example, an antielectron would usually be created at the same time as an electron. The antielectron has a positive charge (it is called a positron), and so the total charge created is zero. (See [link] .) All particles have antimatter counterparts with opposite signs. When matter and antimatter counterparts are brought together, they completely annihilate one another. By annihilate, we mean that the mass of the two particles is converted to energy E , again obeying the relationship $\Delta m=\frac{E}{{c}^{2}}$ . Since the two particles have equal and opposite charge, the total charge is zero before and after the annihilation; thus, total charge is conserved.

## Making connections: conservation laws

Only a limited number of physical quantities are universally conserved. Charge is one—energy, momentum, and angular momentum are others. Because they are conserved, these physical quantities are used to explain more phenomena and form more connections than other, less basic quantities. We find that conserved quantities give us great insight into the rules followed by nature and hints to the organization of nature. Discoveries of conservation laws have led to further discoveries, such as the weak nuclear force and the quark substructure of protons and other particles.

The law of conservation of charge is absolute—it has never been observed to be violated. Charge, then, is a special physical quantity, joining a very short list of other quantities in nature that are always conserved. Other conserved quantities include energy, momentum, and angular momentum.

## Phet explorations: balloons and static electricity

Why does a balloon stick to your sweater? Rub a balloon on a sweater, then let go of the balloon and it flies over and sticks to the sweater. View the charges in the sweater, balloons, and the wall.

## Section summary

• There are only two types of charge, which we call positive and negative.
• Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance.
• The vast majority of positive charge in nature is carried by protons, while the vast majority of negative charge is carried by electrons.
• The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton.
• An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons.
• The SI unit for charge is the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge $\mid {q}_{e}\mid$ is
$\mid {q}_{e}\mid =1.60×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{C}.$
• Whenever charge is created or destroyed, equal amounts of positive and negative are involved.
• Most often, existing charges are separated from neutral objects to obtain some net charge.
• Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another. For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons.
• The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time.

## Conceptual questions

There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?

Why do most objects tend to contain nearly equal numbers of positive and negative charges?

## Problems&Exercises

Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of $–2.00\phantom{\rule{0.25em}{0ex}}\text{nC}$ (b) How many electrons must be removed from a neutral object to leave a net charge of $0.500\phantom{\rule{0.25em}{0ex}}µ\text{C}$ ?

(a) $1.25×{\text{10}}^{\text{10}}$

(b) $3.13×{\text{10}}^{\text{12}}$

If $1\text{.}\text{80}×{\text{10}}^{\text{20}}$ electrons move through a pocket calculator during a full day’s operation, how many coulombs of charge moved through it?

To start a car engine, the car battery moves $3\text{.}\text{75}×{\text{10}}^{\text{21}}$ electrons through the starter motor. How many coulombs of charge were moved?

-600 C

A certain lightning bolt moves 40.0 C of charge. How many fundamental units of charge $\mid {q}_{e}\mid$ is this?

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