# Electricity: Electric Charge, Atoms and Ions, Coulomb’s Law, Electric Field, Electric Field Lines and Potential Difference

## Electricity

In This Chapter:

Electric Charge

Atoms and Ions

Coulomb’s Law

Electric Field

Electric Field Lines

Potential Difference

Electric Charge

Electric charge, like mass, is one of the basic properties of certain elementary particles of which all matter is composed. There are two kinds of charge, positive charge and negative charge. The positive charge in ordinary matter is carried by protons, the negative charge by electrons. Charges of the same sign repel each other, charges of opposite sign attract each other.

The unit of charge is the coulomb (C). The charge of the proton is +1.6 × 10−19 C, and the charge of the electron is −1.6 × 10−19 C. All charges occur in multiples of ±e = ±1.6 × 10−19 C.

According to the principle of conservation of charge, the net electric charge in an isolated system always remains constant. (Net charge means

the total positive charge minus the total negative charge.) When matter is created from energy, equal amounts of positive and negative charge al- ways come into being, and when matter is converted to energy, equal amounts of positive and negative charge disappear.

###### Atoms and Ions

An atom of any element consists of a small, positively charged nucleus with a number of electrons some distance away. The nucleus is composed of protons (charge +e, mass = 1.673 × 10−27 kg) and neutrons (uncharged, mass = 1.675 × 10−27 kg). The number of protons in the nucleus is normally equal to the number of electrons around it, so the atom as a whole is electrically neutral. The forces between atoms that hold them together as solids and liquids are electric in origin. The mass of the electron is 9.1 × 10−31 kg.

Under certain circumstances, an atom may lose one or more electrons and become a positive ion or it may gain one or more electrons and become a negative ion. Many solids consist of positive and negative ions rather than of atoms or molecules. An example is ordinary table salt, which is made up of positive sodium ions (Na+) and negative chlorine ions (Cl).

###### Coulomb’s Law

The force one charge exerts on another is given by Coulomb’s law:

where q1 and q2 are the magnitudes of the charges, r is the distance be- tween them, and k is a constant whose value in free space is

The value of k in air is slightly greater. The constant k is sometimes re- placed by

where ε0, the permittivity of free space, has the value

(ε is the Greek letter epsilon.)

Solved Problem 11.1 Two charges, one of +5 × 10−7 C and the other

−2 × 10−7 C, attract each other with a force of −100 N. How far apart are they?

Solution. From Coulomb’s law, we have

Electric Field

An electric ﬁeld is a region of space in which a charge would be acted upon by an electric force. An electric ﬁeld may be produced by one or more charges, and it may be uniform or it may vary in magnitude and/or direction from place to place.

If a charge q at a certain point is acted on by the force F, the electric ﬁeld E at that point is deﬁned as the ratio between F and q:

Electric ﬁeld is a vector quantity whose direction is that of the force on a positive charge. The unit of E is the newton per coulomb (N/C) or, more commonly, the equivalent unit volt per meter (V/m).

The advantage of knowing the electric ﬁeld at some point is that we can at once establish the force on any charge q placed there, which is

Electric Field Lines

Field lines are a means of describing a force ﬁeld, such as an electric ﬁeld, by using imaginary lines to indicate the direction and magnitude of the ﬁeld. The direction of an electric ﬁeld line at any point is the direction in which a positive charge would move if placed there, and ﬁeld lines are drawn close together where the ﬁeld is strong and far apart where the ﬁeld is weak (Figure 11-1).

Figure 11-1

Solved Problem 11.2 The electric ﬁeld in a certain neon sign is 5000 V/m. What force does this ﬁeld exert on a neon ion of mass 3.3 × 10−26 kg and charge +e?

Solution. The force on the neon ion is

###### Potential Difference

The potential difference V between two points in an electric ﬁeld is the amount of work needed to take a charge of 1 C from one of the points to the other. Thus

The unit of potential difference is the volt (V):

The potential difference between two points in a uniform electric ﬁeld E is equal to the product of E and the distance s between the points in a direction parallel to E:

Since an electric ﬁeld is usually produced by applying a potential differ- ence between two metal plates s apart, this equation is most useful in the form

##### You Need to Know
###### A battery uses chemical reactions to produce a potential difference between its terminals; a genera- tor uses electromagnetic induction for this purpose.

Solved Problem 11.3 The potential difference between a certain thundercloud and the ground is 7 × 106 V. Find the energy dissipated when a charge of 50 C is transferred from the cloud to the ground in a lightning stroke.

Solution. The energy is