Chapter 6 Electrostatics

6.1 Aim

This chapter introduces the reader to the concepts involved in understanding the electrostatics which is relevant to radiographic science. This involves the consideration of electrical charge, charge distribution and electrical potential and potential difference.

6.2 Introduction

Electrostatics, as the name implies, is the study of static electrical charges. We are familiar with many examples of electrostatics from our ordinary lives, from sparks which may occur from our clothes when undressing, to the large discharges of electricity which occur during lightning strikes. Much of the early experimentation with electricity involved electrostatics. It was discovered at an early stage that there were two types of electrical charge, one called negative and the other positive. While it is mathematically convenient to regard charge in this way, it does not explain what electrical charge actually is and how it behaves. This will be the subject of this chapter.

6.3 Properties of electrical charges

The general properties of electrical charges are as follows:

• Charges can be considered as being of two types: positive and negative.

• The smallest unit of negative charge which can exist in isolation is that possessed by an electron, and the smallest unit of positive charge which can exist in isolation is that possessed by a proton.

• Electrical charges exert forces on each other even when they are separated by a vacuum. The forces are mutual, equal and opposite, as expected by Newton’s third law (see Sect. 3.5).

• Like charges (i.e. charges of the same sign) repel each other while unlike charges (of opposite signs) attract each other.

• The magnitude of the mutual forces between the charges is influenced by:

the magnitude of the individual charges

the medium in which they are embedded, being greatest when the medium is a vacuum

the inverse square of the distance between the charged bodies – this is another application of the inverse square law (see Ch. 26).

• Electrical charges may be induced in a body by the proximity of a charged body, leading to a force of attraction between the two bodies.

• Electrical charges may flow easily in some materials (called electrical conductors) and with difficulty in other materials (called electrical insulators). Both types of material are capable of having charges induced in them.

• When electrical charges move, they produce a magnetic field.

6.4 Force between two electrical charges in a vacuum

Consider two charges, q₁ and q₂, separated by a distance, d, in a vacuum, as shown in Figure 6.1.

Figure 6.1 The forces (F) between two electrical charges, q₁ and q₂, separated by a distance (d) are equal and opposite.

If we assume that both charges are of the same sign, then q₁ will exert a force of repulsion (F) on q₂ and q₂ will exert the same force of repulsion on q₁. As we have already stated above, it can be shown that:

Thus, F is proportional to the magnitude of each charge and to the inverse square of the distance separating them.

If we combine the factors in 1, 2 and 3 above, we can produce the equation:

Equation 6.1

If q₁ and q₂ both have the same sign, then F will be positive and will represent a force of repulsion. If the charges have opposite signs, then F will be negative and will represent a force of attraction.

If we wish to replace the proportionality sign in Equation 6.1 by an equals sign then we need to introduce a constant of proportionality (see Appendix A). This equation now reads:

Equation 6.2