Chapter 1

Electric charge and electric forces

Chapter 1

electric charge

The ruler is charged by being rubbed with a cloth towel.

Electrons transfer from the cloth to the ruler, leaving it

with a net negative charge.

This phenomenon is called static electricity. The ancient Greeks knew that a piece of amber would attract small

pieces of leaves or dust or straw , after being rubbed with some wool or a piece of fur.

The excess electric charge on the ruler induces a polarisation (separation of charge) in scraps of paper, and thus attracts them.

Are all electric charges the same, or is there more than one type?

electric charge and its conservation

The law of conservation of electric charge:

whenever a certain amount of charge is produced on one object,

an equal amount of charge of opposite sign is produced on another.

Electric charge can neither be created nor destroyed.

Charge comes in two types, positive and negative; like charges repel and opposite charges attract.

atoms and molecules

Charge on the electron:

In the SI, the unit of electric charge is the Coulomb. Electric charge is quantised in units of electron charge. The total charge carried by any object

is a whole multiple of the electron charge.

e = −1.602× 10−19 C

A polar molecule is neutraloverall, but its charge is not evenly

distributed.

water molecule

Only within the past century has it become clear that an understanding of electricity originates from within the atom itself. This simplified model of an atom shows a small, dense, positively charged nucleus containing a mixture of protons and neutrons surrounded by negatively charged electrons.

All protons and electrons have exactly the same magnitude of electric charge.

insulators and conductors

Conductors

Charge flows freely:

metals

The relative magnitude of conductivity between silver (a good conductor)

and rubber (a good insulator) is on the order of 1021.

Insulators

Almost no charge flows:

most other materials

From an atomic point of view:

• for insulators, the electrons are bound very tightly to the nuclei;

• for good conductors, some of the electrons are bound very loosely and can move freely within the material.

charging methods

Charging by conduction

If a positively charged metal rod is brought into contact

with an uncharged metal rod, the free electrons in the neutral rod

are attracted by the positively charged rod and some will pass over to it.

Charging by induction

If a positively charged metal rod is brought close to an uncharged metal rod, but does

not touch it, the free electrons in the neutral rod do not leave it but move within the metal

rod towards the external positive charge.

electroscope

The electroscope on the left is charged by induction and the one on the right

by conduction.

A previously charged electroscope can be used to determine the sign

of a charged object.

An electroscope is a device used for detecting charge. It is made of two metal leaves that are free to move

(often made of gold), which are situated inside an isolated case.

Coloumb’s law

The French physicist Charles-Augustin de Coulomb (1736-1806) investigated electric forces in the 1780s.

He argued that the force that one charged object (q1) exerts on a second tiny charged object (q2) is directly proportional to the product of their charges

and inversely proportional to the square of the distance separating them (r2).

This equation gives the magnitude of the force. The direction of the force is always along the line joining the two charges.

In SI units, the value of the constant k is:

k = 8.99 x 109 N m2/C2

F kq1 q2

r 2

Coloumb’s law

The magnitudes of F12 and F21

are equal in agreement with Newton’s third law: for every action there is an equal and opposite reaction.

The force always acts along the line connecting the charges: • it is attractive if the charges are of opposite sign; • it is repulsive if the charges are of the same sign.

Calculate the Coulomb force acting on charge q3 shown in the figure due to the charges q1 and q2.

(a)

(b)

a) Direction of the individual forces:

• F32 is repulsive as the force on q3 is in the direction away from q2 because q3 and q2 are both

positive;

• F31 is attractive as q3 and q1 have opposite signs, so F31 points toward q1.

b) The net force F is obtained by adding F32 to F31.

The magnitude of the force is 290 N, at an angle of 65° to the x axis.

Coloumb’s law using vectors

learning the basics

1. In a good conductor, the electrons are bound very tightly to the nuclei. T F

2. When an electroscope is charged, the two leaves repel each other and remain at an angle. T F

3. Coulomb’s law states that the force between two point charges is proportional to the square of the distance separating the charges. T F

jj

jjjj

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applying the concepts

1. Draw the direction and magnitude (qualitatively) of the Coulomb force on each charge due to the other (see the first box for a worked example).

applying the concepts

2. Find:▶ the magnitudes of the Coulomb forces F31 between q3 and q1 and F32 between q3 and q2, and draw their directions on the picture; ▶ the net force on q3.

r F 31 ..............................N

r F 32 ..............................N

r F tot ..............................N