• atttraction and repulsion of electric currents,
• direction of magnetic field of a current,
• explanation of magnetism as due to ``molecular currents''

• Benjamin Franklin (1706-1790) (US politician, diplomat, scientist, writer, printer)
  • lightning as electrical phenomenon
  • lightning rod
  • coined name ``positive'' and ``negative'' for the two kinds of electric charge

• Luigi Galvani (1737-1798) (Prof. of Anatomy at U. of Bologna)

• Alessandro Volta (1745-1827)
  • electrophorus (1775)
  • straw electroscope (1781)
  • condensator (1782)
  • relation between chemical reactions and electricity (1796)
  • ``Voltaic cell'' (battery) (1800)

• Michael Faraday (1791-1867) (bookbinder's apprentice, self-taught chemist and physicist, prof. of physics and chemistry)

• concept of ``electric field'', field lines (lines of force)
• induction (1831)
• basic laws of electrochemistry (1833-1834)
• investigations of dielectrics
• studies of gas discharges
• diamagnetism
• magnetic rotation of plane of polarization of light (1845)

ELECTRIC CHARGE:

• is a fundamental quantity
• is a property of matter which causes a force to act between particles (objects, bodies..) which have this property
• experimental evidence two types of charge (positive, negative)
• charge carried by constituents of matter: electrons and protons

Fundamental carriers of electric charge:

• Matter made up of atoms
• Atoms made up of electrons and nuclei; electrons have negative charge
• Nuclei made up of protons and neutrons
• Protons have positive charge whose magnitude is the same as that of the electrons
• Neutrons have zero net charge

``Normal matter'':

• is electrically neutral (has equal number of protons and electrons);
• electrons can be removed from one material, transferred to another
• net excess of negative charge where electrons added,
• net excess of positive charge where electrons removed.

COULOMB'S LAW:

describes the ``electric force'' (also ``electrostatic force'', ``Coulomb force'') between two bodies with charges , where r is the distance between the two bodies;

• k is a constant, ,
• unit of charge is 1 ``Coulomb'', abbreviated 1 C; 1 C of charge corresponds to the charge of protons. The charge of an electron is Coulombs.
• the force is a vector, its line of action is the straight line connecting the two charges.
• Newton's third law, the force exerted by charge on charge is equal and opposite in direction to that exerted by charge on charge .
• For ``like'' charges, i.e. if the two charges and have the same sign (both positive or both negative), the direction of the forces is away from the other charge (repulsive).
• For ``unlike'' charges (one positive, one negative), the direction of the forces is towards the other charge (attractive).
• Strictly speaking, Coulomb's law as formulated above holds only for ``point charges'', but is approximately also correct for charged bodies whose size is small compared to the distance r between them
• superposition principle:
  the force between any two charges is independent of the presence of all other charges.
  Thus, the net force on any charge is the vector sum of all the forces due to each of the other charges interacting with it independently.

Electrostatic vs gravitational force:

Coulomb's law has same form as Newton's law of gravitation

(mass charge, ),

but electric forces much stronger.

Example:
Forces in hydrogen atom

The hydrogen atom has one electron in orbit around one proton, at a distance

gravitational force between electron and proton:

(remember )

electrostatic force between electron and proton:

( )

Therefore the gravitational force can be neglected at the atomic level.

ELECTRIC FIELD

• ``field of force'': exists in a region of space when an appropriate object (called the ``test object'' or ``probe'') placed at any point in the region experiences a force.
• force depends on a property of the test object (e.g. charge,..), the ``test charge''
• ``field strength''
  = (force experienced by test object) divided by (test charge), = ``force per unit test charge''
• for electrostatic force, this field strength is called ``electrostatic field'' or ``electric field''
• field can be visualized by ``lines of force'' or ``field lines'', which give the direction of the field at every point, i.e.
  the force experienced by a test-charge at any point in space is in the direction tangent to the line of force at that point.
• the density (concentration) of field lines corresponds to the magnitude of the field strength: the denser the concentration of lines, the stronger the field; the farther apart the lines, the weaker the field.
• electrostatic field lines begin on positive and end on negative charges;
• field lines do not cross;
• originally, field lines were invented (by Faraday) as means of visualization, but eventually were regarded as standing for an invisible physical reality - the electric field
• In modern view, all forces (``interactions'') are due to fields, described by ``gauge field theories''.

Electric field of a point charge

Coulomb's law gives force between two point charges.

Formulation in terms of electric field:
the presence of a point-like particle of charge q causes a change in the space around it; it ``generates'' an electric field which permeates all of space.

When a test charge is brought into the field,
the field exerts a force on the test-charge,
given by:

For a positive test-charge, the force points in the same direction as the field.

Comparing with Coulomb's law, we find:

the electric field of a point-charge q is

( is a ``unit-vector'' (i.e. a vector of length 1),
pointing from the charge q to the point at which the field is evaluated).

Extended charged object:
Field due to extended distribution of charges =
sum of the fields due the individual point charges.

• ``lodestone'' (magnetite) known for 1000s of years
• Thales of Miletus studied lodestones (590 BC)
• magnetic compass invented by Chinese around 200 AD
• Pierre de Maricourt a.k.a. Petrus Peregrinus (1269)
  studied magnets, Earth's magnetism; concept of poles, tried to isolate single pole
• William Gilbert (1544-1603) (court physician of Elizabeth I and James I)
  • first serious studies of magnets
  • two ``poles'' of magnets
  • Earth is a magnet
  • iron can be magnetized
  • magnetism destroyed by heating
• Hans Christian Oersted (1777-1851)
  electric current generates magnetic field (1820)

Essentials of magnetism:

• every magnet has two poles - ``dipole''-- there are no magnetic monopoles
• like poles repel each other, unlike poles attract
• magnetic field:
  • magnetic forces due to ``magnetic field'' (Faraday), caused by magnet in its surrounding
  • magnetic field lines describe direction, density of lines represents magnitude of field;
  • field due to one pole obeys ``Coulomb-like'' law, total field of magnetic dipole = superposition of the two fields
  • moving charges (currents) generate magnetic fields

MAGNETISM OF MATERIALS:

• atoms can have magnetic dipole field, partly due to effects of orbital motion of electrons, but mainly due to electron ``spin'' (intrinsic angular momentum of electrons)
• in most materials, atoms have no net dipole field, or directions of elementary dipoles random effects cancel
• in some materials (``ferromagnetic materials''), many atomic dipoles aligned ``magnetic domains''
• if domains not aligned, material is not magnetic; if domains aligned, material is magnetic,
• strong magnetic field can align domains - ``magnetization''
• if domains stay aligned after magnetizing field ``turned off'' ``permanent magnet''
• ``magnetically soft'' materials do not retain magnetization; used for electromagnets

EARTH'S MAGNETIC FIELD

Earth is a magnet

• north-seeking pole of compass needle called (by arbitrary definition) a ``north pole''
• the Earth's northern magnetic pole is actually a magnetic south pole
• Earth's geomagnetic poles are not at geographic poles,
  positions change in time; presently, magnetic N is about 13
  (i.e. about 1500km) from geographic N
• ``declination'' = angle between geographic (true) N and magnetic N;
  15 E in Los Angeles, Las Vegas, Salt Lake City;
  0 in Houston, Tulsa, Omaha;
  2 W in Tallahassee;
  15 W in Boston, Montreal

• point charge q in electric field ``feels'' force
• moving the charge against this force needs work:

  

  (the ``-'' sign is there because the force exerted to move the charge must be opposite to the force due to the electric field)

• the charge gains ``electrical potential energy''
  by an amount equal to , the work done moving the charge
• the electrical potential energy per unit charge is called potential'':

  

• a value of the electric (also called electrostatic) potential V is associated with every point in space; it is a scalar quantity (i.e. a positive or negative number), while the electric field is a vector quantity.

• from the electric potential, the electric field can be derived: it is given by (-) the ``steepness of decrease'' of V when one moves in the direction of its steepest descent:

  

  The direction of is in the direction of steepest descent of V; is the change of V when moving by a distance in the direction of steepest decrease.

• the potential difference between two points A, B in the field numerically
  

  equals the work done against the field moving a unit positive test charge from point A to point B:

  

  The work done can be positive, negative, or zero.

• Only potential (voltage) differences are important -
  not the absolute potential values
  

  electric potential is defined with respect to some arbitrarily chosen zero-point - there is no ``absolute zero of potential''
  usually (but not always):
  potential is defined in such a way that it is zero at infinity.

• potential (difference) is also called ``voltage''
  

• unit of potential or voltage = 1 Volt = 1 J/C
  
• unit of electric field = 1 V/m
  

(Note:
In this section, ``E'' stands for the electric field, not for energy!)

• under influence of the electric field, mobile charges will move towards positions of lower potential energy;
  (positive charges will move toward lower potential, negative charges toward higher potential)
• a conductor is a material which has mobile charges
• when a potential difference is maintained between the ends of a conductor, charges will move ``electric current flows''
• Current:
  electric current = ordered flow of electric charge,
  = rate at which charge moves past a reference point:

  

  unit of current = 1 Ampère = 1A = 1 Coulomb/second

• potential difference (voltage) can be maintained by battery or other `` voltage source'' (often referred to as ``power source'')
• electric circuit
  = assembly of conductors, voltage sources and other ``circuit elements''
• ``Ohm's law'' relates the current to the applied voltage:

  

  ``current = voltage / resistance '',
  where ``resistance'' is a measure for the opposition against charge flow within the conducting material (e.g. due to collisions with atoms, other charge carriers,..)

• unit of resistance = 1 ohm = = 1 V/A
• due to resistance, not all electric potential energy is converted into kinetic energy of charge carriers and eventually useful work - some (or all) of it is ``dissipated'' as heat

• power consumption in a circuit:
  • when current is allowed to flow, charges move from higher potential energy to lower potential energy;
  • total change in potential energy =
    amount of charge moved voltage =
  • this change in potential energy can be used to do work and/or is converted into heat.
  • loss in potential energy has to be made up by energy supplied from the power source:
    

    

    So, the power consumption P in a circuit is given by

    

    

Historical notes:

• Georg Simon Ohm (1789 -1854) (Prof. Physics in Munich)
  - Ohm's law of electricity
  - Ohm's law of acoustics

SUMMARY OF IMPORTANT FACTS:

• electric current: = ordered flow of electric charge,
  = rate at which charge moves past a reference point:

  

• electric potential, voltage
  

  

• the potential difference (=voltage difference) between two points A, B in the field numerically equals the work done against the field moving a unit positive test charge from point A to point B:
  

  

  The work done can be positive, negative, or zero.
  

• Only voltage differences are important - not the absolute voltage values
• Under the influence of a voltage ( electric field) applied across a conducting medium, a current (of positive charges) flows from higher to lower voltage. The potential energy lost by the charges is converted into work and/or heat, and has to be replenished by the ``power source''.

• The power consumption P in a circuit is given by

  

• ``Ohm's law'' relates the current to the applied voltage:

  

  ``current = voltage / resistance '',
  

• units of some electrical quantities:
• unit of current = 1 Ampère = 1A = 1 Coulomb/second
• unit of potential or voltage = 1 Volt = 1 J/C
• unit of resistance = 1 ohm = = 1 V/A
• unit of electric field = 1 V/m