The idea that matter is made of atoms was suggested by the Greek philosopher Democritus, who lived in the fifth century BC.  Democritus did not have much in the way of physical evidence that matter consisted of atoms.  But experiments by chemists in the 19th century gave strong evidence that matter indeed consisted of atoms.  In the 20th century the modern picture of the atom emerged.

There are some ninety stable atoms that make up all matter on earth.  An atom consists of a heavy nucleus surrounded by light electrons.  The nucleus is a composite particle, but the electrons are thought to be elementary particles.  Nearly all the mass of an atom is concentrated in the nucleus, which is made up of protons and neutrons.  Protons and neutrons are called nucleons.  The mass of a nucleon is approximately 2000 times larger than the mass of an electron.  Protons and electrons are charged particles.  Just like mass, charge is a fundamental property of the elementary particles that make up all matter.

Properties of charge:

There are two kinds of charge, which we label positive and negative.  The SI unit of charge is C = Coulomb.  The charge of a fundamental particle may be positive or negative, but its magnitude is always an integer multiple of the fundamental quantity e = 1.6 ´10^-19C.  Unlike mass, charge is quantized.  The electric charge of the nucleus is positive, the charge of the electron is negative.  Each electron has a charge of -e = -1.6 ´10^-19C, each proton has a charge of e = 1.6 ´10^-19C.  Neutrons have no charge.  The net charge of a system of particles is the sum of the charges of all the particles in the system.  If we combine equal amounts of positive and negative charge we obtain zero net charge.  The net charge of a system is a conserved quantity.  Net charge cannot be created or destroyed.  We say that charge is conserved.

Atoms are neutral particles.  They have no net charge.  The charge of the nucleus is exactly canceled by the charge of the electrons.  We have exact cancellation, because charge is quantized.  The "atomic number" Z of an atom gives the number of protons in the nucleus.  The number of electrons in a neutral atom equals the number of protons.  The charge of the nucleus is Ze.  The "atomic mass" A gives the total number of nucleons.  The number of neutrons is A-Z.  Chemical and structural properties of matter are determined by the way electrons are arranged in various atoms and how atoms combine to make molecules or other structures.  The number of atoms in ordinary matter is extremely large.  For example 18 grams of water consist of about 6´10²³ atoms of oxygen and twice that many atoms of hydrogen .

The net charge of an object is the sum of the charges of all the particles that make up the object.  Since a neutral atom is made up of an equal number of protons and electrons its net charge is zero.  The net charge of ordinary matter, composed of neutral atoms, is zero.

Problem:

Link:

Massive particles interact via the gravitational force.  A particle with mass m₁ exerts a force F₁₂ on a particle with mass m₂.  Newton's law of gravitation gives this force as

.

Here r₁₂ is the distance between particles 1 and 2, and = r₂-r₁/|r₂-r₁| is the unit vector pointing from particle 1 to particle 2.  G is the gravitational constant, G = 6.67´10^-11Nm²/kg².

The force F₂₁, which the particle with mass m₂ exerts on the particle with mass m₁, is equal to -F₁₂, according to Newton's third law.  The gravitational force is always attractive.

Charged particles at rest interact via the Coulomb force.  A particle with charge q₁ exerts a force F₁₂ on a particle with charge q₂.  Coulomb's law gives this force as

.

The constant k_e is k_e = 9´10⁹Nm²/C².  It is often written as k_e = 1/(4pe₀), where e₀ = 8.85´10^-12C²/(Nm²) is called the permittivity of free space.

The force F₂₁, which the particle with charge q₂ exerts on the particle with charge q₁, is equal to -F₁₂, according to Newton's third law.  Two positively charged particles repel each other.  Two negatively charged particles repel each other.  But a positively charged particle and a negatively charged particle attract each other.

Problems:

The total force on an object is the vector sum of all the forces acting on it.  The total electric force is the vector sum of all the electric forces acting on the object.  Assume we have 4 charged particles.  Then the total electric force acting on particle 1 is

F₁ = F₂₁ + F₃₁ + F₄₁

.

This is called the principle of superposition.

Problem:

If atoms are electrically neutral and ordinary matter is composed of atoms, how can we observe the interaction between charged objects on a macroscopic scale?

Charge cannot be created or destroyed, but charge can be separated.  In atoms, the outermost electrons are bound to the nucleus by the weakest force.  They have the largest distance from the nucleus, and they are also repelled by the inner electrons.  Some atoms attract their outermost electrons more strongly than other atoms.  For example, atoms in rubber attract their outermost electrons more strongly than atoms in wool.  When a rubber rod is rubbed with wool, electrons near the surface are attracted more strongly to the rubber than to the wool, and some electrons are transferred from the wool to the rubber.  The rubber becomes negatively charged and the wool becomes positively charged.  When enough electrons have been transferred, then the wool becomes more attractive and the rubber more repulsive to additional electrons, and the transfer stops.  This phenomenon is called triboelectricity or contact electricity.

The triboelectric sequence classifies materials according to the ease with which they become electron donors or acceptors.  Materials can also be classified according to the ease with which electrons can freely move through the material.

In some materials the outer electrons are firmly bound to their respective nuclei.  They can be pulled more towards one or the other side of the nucleus they are bound to, but they cannot leave it.  Those materials are called insulators.  In other materials the outermost electrons are free to move through the material.  They cannot easily leave the material but can move freely from atom to atom.  Those materials are called conductors.  Some materials are insulators at low temperatures, but become conductors as the temperature is raised.  The number of electrons that can freely move through the material increases with temperature.  Those materials are called semiconductors.

Link:  Balloons and Static Electricity

The electric field

In the presence of other charges, a charge q is acted on by a net force F, which is the vector sum of the forces due to all the other charges.  We define the electric field due to the other charges at the position of the charge q as E = F/q.  To measure the electric field at a point P due to a collection of charges, we can bring a small positive charge q to the point P and measure the force on this test charge.  The test charge must be small, because it interacts with the other charges, and we want this interaction to be small.  We divide the force on the test charge by the magnitude of the charge to obtain the field.

If a point charge Q is located at the origin then a test charge q at position r experiences a force

.

The electric field due to Q at r therefore is

.

If Q is positive, then the electric field points radially away from the charge.

If Q is negative, then the electric field points radially towards the charge.

We obtain the electric field due to a collection of charges using the principle of superposition. 
E = E(Q₁) + E(Q₂) + E(Q₃) + ¼ .

Links:

Field Lines

Field lines were introduced by Michael Faraday to help visualize the direction and magnitude of he electric field.  The direction of the field at any point is given by the direction of the field line, while the magnitude of the field is given qualitatively by the density of field lines.  The field lines converge at the position of a point charge.  Near a point charge their density becomes very large.  The magnitude of the field and the density of the field lines scale as the inverse of the distance squared.  Field lines start on positive charges and end on negative charges.

Rules for drawing field lines:

Examples:

Problem:

Forces and fields due to continuous charge distributions

Even though charge is quantized, we often can treat it as being continuously distributed inside some volume, since one quantum of charge is a tiny amount of charge.  On a macroscopic scale we define the volume charge density r = lim(DQ/DV) = dQ/dV as the charge per unit volume.

We then have for the electric field of a distribution of charges

.

Here is the unit vector pointing from r_i to r, and is a unit vector pointing from the volume element dV' at r' to r.

If the charge is distributed over a surface, then rdV Þ sdA, where s is the surface charge density and dA is an element of surface area.  For a line charge distribution we have rdV Þ ldl, where l is the line charge density and dl is an element length.

Problem:

Link to other Web Material:

Please complete assignment 8 now.  For the User ID use your registered password.

You can submit the assignment up to three times.  Each time the computer will tell you your score.