# CHARGES AND FIELDS

 Contents for this page Related topics Charge Coulomb's law Conservation of charge Conductors and insulators The electric field Electric field lines     Worked example 1     Worked example 2 The energy of a charge in a field Millikan's oil drop experiment Data Glossary Learning Outcomes After studying this section, you will (a) be familiar with the concept of charge and know and be able to apply Coulomb's law, (b) know that the algebraic sum of charges are conserved during charge transfer, (c) know the difference between conductors and insulators, and (d) understand the concepts of electric field and electric field lines.

## Charge:

Some objects have a scalar property called charge. Charge can be either positive (denoted by "+"), or negative (denoted by "-").

Objects which have like charges repel one another.

Objects which have unlike charges attract one another.

The symbol for the charge on an object is Q (or q), and the unit of charge is the coulomb, (C).

## Coulomb's law

Two charges will exert a force on each other (either a force of attraction or a force of repulsion, depending on the charges):

The force F between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them, r2.

The constant of proportionality, k, is called Coulomb's constant, and has the value of 9 x 109 N.m2.C-2.

## Conservation of charge:

Charge can be transferred from one object to another. The algebraic sum of the charges on the two objects will be the same before and after the transfer. (This is sometimes called the Law of Conservation of Charge, discovered by Benjamin Franklin).

If Q1 and Q2 are the charges on two objects 1 and 2, then if a transfer of charges takes place, and the new charges are Q1' and Q2', then

The subatomic particle which has a single positive charge is called the proton. Its charge is 1.60210 x 10-19 C.

The subatomic particle which has a single negative charge is called the electron. Its charge is 1.60210 x 10-19 C.

## Conductors and insulators:

Materials through which electrons are able to move are known as conductors. Metals tend to be good conductors. Solutions of salts, known as electrolytes, also conduct electricity.

Materials through which electrons cannot move are called insulators. Examples of insulators are glass and rubber.

## The electric field:

An electric field is a region in space in which an electric charge experiences a force.

 The strength of such a field at a point in space is defined as the force exerted on a positive charge at that point, divided by the magnitude of the charge, i.e.,

E, the electric field strength, is a vector quantity and its direction is the same as that of the force. It has units newtons per coulomb, N.C-1.

A charged spherical particle will create an electric field. The strength of the field, E, is proportional to the magnitude of the charge Q, and inversely proportional to the square of the distance, r, from the centre of the particle.

 At the point P,     E = kQ/r2where k is Coulomb's constant.

If a field is due to more than one charge, Q1, Q2, Q3 ... and so on, the individual fields E1, E2, E3..., due to each of the charges may be added vectorially at a point to produce the resultant field:

## Electric field lines:

Electric field lines are imaginary lines along which a small positive test charge would move.

The force experienced by the positive test charge is always in the direction of the tangent to the field line.

Electric field lines have the following properties:

1. They start on a positive charge and end on a negative charge.
2. They never cross.
3. They are closer together in regions where the field is stronger and further apart where the field is weak.
4. They begin and end perpendicularly to the charged surface.

Of course, field lines as represented on this screen or on paper are inaccurate illustrations of the electric field because:

1. the field is continuous, while one draws the lines at discrete intervals
2. the field is three-dimensional, while the field as we draw it is a representation of a two-dimensional section through the field.

## Definition of electric field:

 Measuring the field strength at a point using a test charge presents a problem, as the charge has a field and this field will add to the field being measured. Thus we need to use a test charge which is very small or approaching zero.

## The vector nature of force and electric field:

a. Charge is a scalar quantity.

b. Force is a vector quantity.

c. The presence of a charge creates an electric field in space, the strength of which is a vector quantity.

d. The force between two positive charges is directed along the line joining these charges.

e. If the sign of the charges is included in calculations of the force between two charges using Coulomb's Law, then the forces which have a negative sign are attractive and those which have a positive sign are repulsive.