Electric charge

Coulomb’s law

Electric field

ELECTRICITY Lecture 3.7

ELECTRICITY

Many important uses Light Heat Rail travel Computers Central nervous system

Human body made up of electric charges. Atoms contain positive and negative charges

Atoms bound together by electric forces » molecules

Molecules interact to produce bones, blood, skin, etc

Interaction between electrically charges objects

ELECTRICITY

Historical 6th century B.C., Greeks noticed sparks were produced when the fossilized tree resin called amber was rubbed with fur.

Greek word for amber is elektron from which the word electricity is derived. Major discovery 1861: Maxwell’s equations. Unified electric and magnetic phenomena (electromagnetism).

End of the 19th and early 20th century: Fundamental discoveries concerning the electronic structure of the atom were made.

Electric charge is a characteristic of sub-atomic particles.

An atom is composed of 3 kinds of particles: protons , electrons and neutrons.

Electric charge and the atom

Simple View

e e

e

Nucleus

Neutrons Protons

Atom

Particle Charge Value (SI unit)

proton +e 1.6 x 10-19 Coulomb (C)

electron -e -1.6 x 10-19 Coulomb (C)

neutron none -----------------

These particles are, in general, neither created nor destroyed, but electrons can be displaced from one atom to an other.

Electric charge and the atom

Nucleus Carbon Atom

6 protons: charge +6e 6 neutrons: (no charge)

Atoms are electrically neutral -

-

- -

-

-

6 electrons: charge -6e

Electron removed – result positive ion Electron added – result negative ion

Total positive charge of the nucleus

total negative charge of the electrons around the nucleus.

=

Electric charge and the atom

Electric charge is a basic physical property of subatomic particles, protons and electrons.

3 Properties of charge

1. Two types of charges, positive and negative

2. Charge is conserved. Cannot be created or destroyed. Charges can be separated.

3. Like charges repel and unlike changes attract

Electrostatic forces result from the separation of positive and negative charges.

Electric charge Electrically charged materials

Balloon and wool rubbed together: balloon becomes negatively charged

Many examples

Plastic comb run through your hair comb will then attract bits of paper

Almost any two non-conducting substances when rubbed together will become charged

Friction associated with rubbing does not create the charge Charge transferred by movement of electrons

Charge is conserved Neither created or destroyed

Total amount of charge in universe: constant

- - - - -

- - - - - - -

- - - - -

-

+

+ + +

+ +

Electric charge

Basic unit of positive charge: +e = 1.6 x 10-19 Coulomb

Basic unit of negative charge: -e = -1.6 x 10-19 Coulomb (C)

Any charged object:

•Total charge is always a multiple of e

•Never fractional charge

•Charge can only have values ±e, ±2e, ±3e ±..

•Charge is said to be quantised

Coulomb’s Law

Charge on an electron = -1.6x10-19C

= 6.25x1018 electrons are required to make up a charge of 1 Coulomb.

-1.6x10-19C

-1C therefore

Example. How many electrons are required to make up a negative charge of one Coulomb?

Fundamental quantity of charge found in matter is that associated with a proton (+e) and electron (-e)

Electric charge

Conductors- •Example: metals, copper etc. •charges are free to move.

Types of Materials

Insulators- •Example: Rubber, plastic etc •charges are not free to move.

Semiconductors- • Example: Silicon, Germanium •movement of charges can be controlled by temperature or doping of the material. Application: electronic devices

Photoconductors: •Example: Selenium •In darkness: Insulator •Exposed to light: conductor •Application: photocopier, laser printer

Electric charges and forces Coulomb’s law Mathematical law that describes how •like charges repel •unlike charges attract

+ + q1 q2 F F

r

+ - q1 q2 F F

r

Unlike charges

- - q1 q2 F F

r

Like charges

1 22

q qFr

∝

Coulomb’s law: “the force between two point charges is proportional to the product of their charge and inversely proportional to the square of their separation”

Direction of the force: along line joining the point charges.

Charles Coulomb (1736-1806) French physicist,

1 22

q qF kr

=1 22

q qFr

∝

Coulomb’s Law

SI unit of charge is called the Coulomb

Force F is known as the Coulomb force or electrostatic force and its units are Newtons

distance r is in metres Hence units of k are Nm2C-2

The constant k is determined by experiment to be 9x109 Nm2C-2 (in a vacuum)

Coulomb is a very large quantity of charge

The constant k is frequently written as

where ε0 is called the permittivity of free space 0

14

kπε

=

12 2 1 20 8.85 10 C N mε − − −= ×

Coulomb’s Law

Coulomb force is very large compared with gravitational force

Example: Two charges, each of one Coulomb, are a distance of 1 metre apart. What is the force between them?

1 22

0

14

q qFrπε

=1C∗ 1C 4π 8.85x10-12C2N-1m-2 ∗1m∗1m =

F = 9x109 N = 9 billion Newtons

Example Coulomb Force

e0 = 8.85 × 10-12 C2N-1 m-2

mass of an electron = 9.11 × 10-31 kg G = 6.67 × 10-11 N m2 kg-2

Compare electrostatic repulsive force between two electrons held one metre apart in a vacuum and the gravitational force of attraction between them?

Coulomb force

1 22

m mF Gr

=Gravitational force

F = 2.3 x 10-28 N

F = 5.5 x 10-71 N

1 22

0

14

q qFrπε

=

1.6 x10-19C∗ 1.6x10-19C 4π 8.85x10-12C2N-1m-2 ∗1m∗1m

F =

( )211 31

2

6.67 10 9.11 101

F− −× ×

=

Coulomb’s Law

+ - F -F

r Proton q =+e

Electron q= -e

Electron and proton, a distance r apart, are simultaneously released from rest. Where do they collide?

Newton 3rd law, forces are equal and opposite

Collision at midpoint ??

acceleration Newton 2nd law F = ma

a = F m

electron mass = 9.11 × 10-31 kg proton mass = 1.67 × 10-27 kg

Mass of proton ≈ 1833 times mass of electron acceleration of electron 1833 times greater

Coulomb’s Law

Collide very near initial position of proton

20

12

x v t at= + 212p px a t=

212e ex a t=

e e

p p

x ax a

= //

pe e

p p e

mx F mx F m m

= =

-27

-31

1.67 10 k 18339.11 10 kg 1

e

p

x gx

×= =

×

1833e px x=

+

r

-

Electric Field Electrostatic force and gravitational force can both act through space even when there is no physical contact between the objects involved.

An electric field exists in a region of space around a charged object.

In the case of charged particles, what transmits the force between them?

Gravitational field: g

F = mg

Potential Energy ∆U ≈ mgh

m

mass m experiences a force:

Field lines show the direction of the force and indicate its relative magnitude

Electric field near a negative charge is directed radially into the charge as shown

Electric field near a positive charge is directed radially out from the charge

-

Electric Field

Electric field lines show • direction of the force • indicate its relative magnitude

Similar to gravitational field lines

2+

Electric field lines

Double the charge Double the number of field lines

+

Consider positive test charge q0(fictitious) at A

- A + A +

Electric Field

Consider force on positive test charge

Assume test charge is small and does not affect any other charges

+

q0 q0

Electric field represents the electric force a stationary positive charge experiences.

Test charge: helpful in determining forces generated by other charges

The electric field E is said to exist in the region of space around a charged object.

Example:

Electric Field

+ + +

+ + +

+

+ + + +

+

Q

Electric field E due to charge Q at location of small test charge q0 is given by;

SI unit of electric field

+ q0

Test charge

0

FEq

=

F is the force exerted on q0 by Q

Newton per coulomb (NC-1)

Electric force per Coulomb

Electric Field

02

0

14

QqFrπε

=

20

14

QErπε

=

0Eq=

Electric field at a given point depends only on the charge Q on the object setting up the field and the distance r from the object to the specific point in space

Analogous to F= mg in gravitational field

0

FEq

= 0F q E=

Determine the electric field at A, a distance of 40cm from a positive charge Q of 2x10-3 Coulombs

+ Q

r

A E

Find field E at point A 40 cm from Q.

2

QE kr

=

E= 9 x 109 N.m2C-2 (2 x 10-3) C (0.4m)2

E = 112.5 x106 NC-1

Example

Electric Field

Example How many electrons must be removed from an object so that it is left with a charge of 8 x10-10 C

Total charge = 8 x 10-10 C

Charge on electron = -1.6 x 10-19 C

Therefore number of electrons removed

= 8 x 10-10 C

1.6 x 10-19 C = 5 x 109 electrons

Electric charges

Example

Determine the minimum distance apart two identical charges of 0.1 C must be in order that the Coulomb force between them is less than 500 N. k = (9 x 109) Nm2C-2

1 22

q qF kr

=

Coulomb force

420r m

( )9 2 2

2

9 10 0.1 0.1500

Nm C C CN

r

−× ×

( )92 9 10 0.1 0.1

500r

× ×

( )99 10 0.1 0.1500

r× ×

An object has a total charge of -2 x10-6 C. How many excess electrons does the object have.

Total charge = -2 x 10-6 C

Charge on electron = -1.6 x 10-19 C

Therefore number of excess electrons

= -2 x 10-6 C

-1.6 x 10-19 C = 1.25 x 1013 electrons

Electric charges

Example