Chapter 1

Electrostatics

The Electric Charge

Electric charge, or ’electricity’, can come from batteries and generators. But some materials

become charged when they are rubbed. Their charge is sometimes called electrostaticcharge or ’static electricity’. It causes sparks to jump from your finger to a metal doorknob

after you walk across a wool carpet.

Figure 1.1:

2

3

1.0.1 Negative and Positive charges

Figure 1.2: Attraction and Repulsion

There are two distinctly different types of electric charges. These were given the arbitrary

names positive and negative by Benjamin Franklin. One may observe that, when comparing

objects bearing these different charges, like charges repel each other and opposite charges

attract each other.

1.0.2 Where charges come from

Everything is made of tiny particles called atoms. These have electric charges inside them.

A simple model of the atom is shown below. There is a central nucleus made up of protonsand neutrons. Orbiting the nucleus are much lighter electrons:

Electrons have a negative (-) charge.

Protons have an equal positive (+) charge.

Neutrons have no charge.

Figure 1.3:

4 CHAPTER 1. ELECTROSTATICS

Normally, atoms have equal numbers of electrons and protons, so the net (overall)

charge on a material is zero. However, when two materials are rubbed together, electrons

may be transferred from one to the other. One material ends up with more electrons than

normal and the other with less. So one has a net negative charge, while the other is left with

a net positive charge. Rubbing materials does not make electric charge. It just separates

charges that are already there.

Figure 1.4:

1.0.3 Conductors and Insulators

Different materials have varying abilities to conduct electrical charge. Those that allow

electric charges to move freely are called conductors, and those that do not transport

charges freely are called insulators.

When some materials gain charge, they lose it almost immediately. This is because

electrons flow through them or the surrounding material until the balance of negative and

positive charge is restored. Conductors are materials that let electrons pass through them.

Metals are the best electrical conductors. Some of their electrons are so loosely held to

their atoms that they can pass freely between them. These free electrons also makes metals

good thermal conductors. Good conductors include carbon and metals (especially silver,

copper and aluminium). Poor conductors include water, the human body and the earth.

5

In an insulator the electrons are tightly held to atoms and are not free to move - al-

though they can be transferred by rubbing. Insulators are easy to charge by rubbing be-

cause any electrons that get transferred tend to stay where they are. Common insulators

include plastics, glass and rubber – when such materials are rubbed, only the area rubbed

may change in charge.

Thus, if you hold and rub rods of polythene and copper, the polythene may attract paper

because its surface is charged, but the copper will not, since the charge you rub into it will

become dispersed throughout your body.

A different type of material is the semiconductor. Semiconductors include silicon and

germanium, and their electrical properties can be changed by adding various amounts of

foreign atoms to the material. They are poor conductors when cold, but much better con-

ductors when warm. These semiconductive properties make possible most of the technol-

ogy invented in the last twenty years.

1.0.4 Attraction of uncharged objects

A charged object will attract any uncharged object close to it. For example, the charged

screen of a TV will attract dust.

Figure 1.5:

The diagram above shows what happens if a positively charged rod is brought near a

small piece of aluminium foil. Electrons in the foil are pulled towards the rod, which leaves

the bottom of the foil with a net positive charge. As a result, the top of the foil is attracted

6 CHAPTER 1. ELECTROSTATICS

to the rod, while the bottom is repelled. However, the attraction is stronger because the

attracting charges are closer than the repelling ones.

1.0.5 Induction

If the earth can be considered an infinite sink for electrical charge, and a conductor is

connected to the earth, the object is said to be grounded or ’earthed’. Building on this idea,

we can see how a conductor may become charged by a process called induction.

When, for example, a positively charged rod is brought near (not touching) a neutral,

non-grounded sphere, the electrons in the sphere near the rod will migrate towards the rod.

However, if the sphere is grounded, some of the electrons will migrate from the earth.

Then, when the ground is removed, the sphere retains an induced negative charge. When

the rod is removed, the positive charge is distributed evenly within the sphere. Throughout,

the rod loses none of its charge.While

charging

by in-

duction

does not

require

contact,

charging

by con-

duction

does nec-

cessitate

contact.

Insulators can undergo a process similar to charging by induction called polarization.

In this case, the presence of a charged external object causes charges within individual

molecules to realign in an insulator. This is why things like combs and balloons can attract

neutral object after being rubbed.

Figure 1.6:

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Coulomb’s LawWhen

inputing

the values

for the

charges

in Equ.

1.1 only

put the

magni-

tude and

NOT the

sign.

Coulomb’s law is based on experiments which verified that the electric force between two

particles is proportional to the product of the charges q1 and q2 of the two particles and

inversely proportional to the square of their separation r. It is attractive if the particles have

like charges and repulsive if charges have a different sign.

F = k|q1| |q2|

r2 (1.1)

Where k is a constant which depends on the unit used for charge. In SI, this unit is

the coulomb (C), which is defined in terms of a unit current called the ampere (A), current

being the rate of flow of charge. If the current passing through a wire is 1A, the amount of

charge which will pass through any point on that wire in one second is 1C. So, in SI, the

coulomb constant is:

k = 8.9875×109 N ·m2

C2 (1.2)

(k is often approximated as 9.0×109 for simplicity in calculations.) The constant can

also be written as:

k =1

4πε0(1.3)

Where ε0 is the permittivity of free space and is:

ε0 = 8.8542×10−12 C2

N ·m2 (1.4)

Note that electromagnetic forces are still vectors.

S. S. Calbio http://www.izifundo.weebly.com 2015

BISHOP ANSTEY HIGH SCHOOL & TRINITY COLLEGE EAST

SIXTH FORM

CXC CAPE PHYSICS, UNIT 2

Ms. S. S. CALBIO – Homework #1

Question 1 & 2 Due: 3rd September 2015 @ 10:45am, Question 3 is a bonus.

Electric Fields

http://izifundo.weebly.com/objective-3-electric-fields.html

1) Interact with the PHET Simulation of John Travolta and explain (in approx. one

paragraph) what is occurring and why.

2) Force between charges

The figure to the right shows three small

charges A, B and P in a line. The charge at A is

positive, that at B is negative and that at P is

positive. The values are those shown.

(a)Calculate the force on the charge at P due to A and B.

(b)At what point X on the line AB could there be no force on the charge P due to A and B if

P were placed there?

3) Force between charges

In the figure to the right, two small equal charges 2 x 10-8C

are placed at A and B, one positive and the other negative.

AB is 6cm.

Find the force on a charge +1 x 10-8C placed at P, where P is 4cm from the line AB along

the perpendicular bisector XP.