Text of Electrostatics – magnetism - electricity – electromagnetism Chinese document magnetism Ancient...
Electrostatics magnetism - electricity electromagnetism Chinese document magnetism Ancient Greeks Static electricity Elektron (Amber) Ancient Greeks Magnetism Magnetite found in Magnesia district William Gilbert Shows electrostatics occurs generally Michael Faraday and Joseph Henry Induction of current by relative motion of magnet and conductor Heinrich Herz Verifies ME by experiment James Clark Maxwell Maxwells Equations EM waves with v = c Charles Coulomb 2000 BC700 BC Hans Oersted Deflects compass by electricity Robert Millikan Q = Ne 16001831187317851888190920041819 New results Active research and applications Dr SH Connell (76826) 082 945-7508 School of Physics, http:www.src.wits.ac.za/~connell
Electrostatics (9 lectures) Charges Insulators and Conductors23-1,2 Coulombs Law23-3 Electric Field and its calculation23-4,5 Lines of force23-6 Electric flux, Gausss theorem and applications24-1,2,3,4 Electric Potential and potential difference25-1 Relation between electric potential and field (1D)25-2 Equipotential surfaces25-1,6 Electron volt as a unit of energy25-1 Electric potential of a point charge and charge distributions25-3 Van de Graaff generator25-8 Definition of capacitance26-1 Parallel plate cylindrical capacitors26-2 Capacitors in series and parallel26-3 Energy of a charged capacitor26-4 Current Electricity (7 lectures) Electric current, current density27-1 Drift velocity and microscopic view of currrent27-2 Ohms Law and resistance27-2 Resistivity and conductivity; temperature variation27-4 Electric Power27-6 Resistors in series and parallel28-2 Emf and terminal voltage28-1 Kirchoffs laws and their applications28-3 Ammeters and voltmeters, determination of resistance28-5 Wheatstone bridge and slidewire bridge28-5
Electrostatics is an active field
STATIC ELECTRICITY CURRENT ELECTRICITY ELECTRO- MAGNETISM Stationary charges Insulators Moving charges Conductors (semiconductors) Due to currents (magnetic materials) Forces fields Potential Energy Capacitance Batteries & circuits Energy conversion Resistance Forces fields Generate currents Inductance
+ve nucleus N protons Charge = +Ze nuclear diameter 10 -15 m (Rutherfords exp) Electron charge -e N electrons Charge = -Ze Atomic diameter 10 -10 m (Einsteins analysis of Brownian Motion) Shell model of the Atom small +vely charged nucleus surrounded by e - in planetary orbits normal atom is neutral The atom is mostly empty space
1.Insulators can be charged by conduction 2.Conductors can be charged by induction 3.There are two types of charges a)Like charges repel b)Unlike charges attract 4.Benjamin Franklyns convention, when rubbed with fur a)Glass acquires a +ve charge b)Rubber acquires a ve charge 5.Charge is conserved (not created or destroyed) a)Charging results from separation and transferal of charges 6.Definition of charge MKS/SI unit of charge is the Coulomb (C) The charge that results from a flow of current of 1 Amp for 1 second. 7.Charge is quantised, q = Ne, e = 1.602 x 10 -19 C 8.Materials come in three types a)Conductors (Charge moves freely : Cu, Al, .) b)Insulators (Charge is not mobile : glass, rubber ) c)Semiconductors (Intermediate behaviour, Si, Ge ) The Basics (Serway 23-1,2,3,4,5,6) How do we know about static electricity ? Make sense of experiments .
Triboelectric series Rabbits fur Glass Mica Wool Cats fur Silk Cotton Wood Amber Resins Metals (Cu, Ni, Co, Ag, etc) Sulphur Metals (Pt, Au, etc) Celluloid + _ When two materials are rubbed against each other, the one higher in the chart will lose electrons
There are two types of charges, positive and negative Like charges repel, Unlike charges attract
Charging by induction Neutral metal sphere Induced redistribution of charge NB : No contact ! Remove ground connection Excess charge remains Partial discharge by grounding
A charged object induces near-surface charge in an insulator Atoms or Molecules near the surface are induced to become partial temporary dipoles This is the mechanism by which the comb attracts the paper
Coulombs Torsion Balance Twist measures repulsive force Coulombs Law Coulomb showed experimentally that the electric force between two stationary charged particles is 1.Inversely proportional to the square of the separation of the charged particles and directed along the line joining them 2.Directly proportional to the product of the two charges. 3.Attractive for unlike charges and repulsive for like charges. If F is in Newtons, q 1 and q 2 in Coulombs and r in meters, then, = permittivity of free space = 8.86 x 10 -12 C 2 N -1 m -2 or Farads.m -1 then k = 1/4 0 = 9 x 10 9 mF -1
The resultant force in a system of many charges Force is a vector quantity. The force between two charges is +q 1 -q 2 and attractive (repulsive) for an overall -ve (+ve) sign. q 1 q 2 < 0 attractive force The Principle of Superposition If there are more than two point charges, then Coulombs Law holds for every pair of charges. Let the charges be q 1, q 2, q 3, q 4, q n, . Then the resultant force on q n is given by the vector sum See Examples .
Coulombs Law example 1 Find the resultant force (and direction) on q 1 q 3 = -2.0 C q 1 = -1.0 C q 2 = +3.0 C 15 cm 10 cm y x 30
The Hydrogen Atom Compare the electrostatic and gravitational the forces (The average separation of the electron and proton r = 5.3 x 10 -11 m ) +Ze e F v r F e /F g = 2 x 10 39 The force of gravity is much weaker than the electrostatic force What other fundamental differences are there ?
Coulombs Law example 2 A certain charge Q is to be divided into two parts, q and Q-q. What is the relationship of q to Q if the two charges, placed a given distance apart, are to have a maximum coulomb repulsion ?
The Electric Field The electric field E at a point in space is defined as the electric force F, acting on a positive test charge q 0, placed at that point divided by the magnitude of the charge. Note that the electric field E is produced by some other charge external to the test charge q 0. The existence of an electric field is a property of its source Every charge comes with its own electric field. The electric field will exist regardless of its magnitude and direction being measured with a test charge. Units NC -1 or Vm -1 It follows that
Electric field lines These are a way of visualizing the electric field. The electric field vector E is tangential to the electric field line at any point. The magnitude of the electric field vector E is proportional to the density of the lines. Electric field lines can never cross. For a positive point charge, the lines are directed radialy outward. For a negative point charge, the lines are directed radialy inward. An electric dipole has two nearby point charges of equal magnitude q and opposite sign, separated by a distance d. The number of lines leaving the positive charge equals the number of lines entering the negative charge.
The electric field lines of two neighbouring positive point charges is as shown in the figure. At large distances, they will approximate the electric field lines a a single point charge of magnitude 2q. Example 3 Show that the density of electric field lines around a point charge is consistent with the expression for the electric field arising from Coulombs Law.
Calculating the Electric Field due to a point charge at a distance r Place a point charge q 0 a distance r from the charge q Now calculate the electric field from the definition The unit vector r lies along the line joining the point charge and the test charge, with a direction indicating the direction the point charge would move. For the electric field due to a system of point charges, calculate the electric field vectors individually, and add them vectorially using the Principle of Superposition. + + q q0q0 r F
The electric field on the axis of an electric dipole Consider the situation as shown in the figure, with y >> a. The dipole moment is defined as p = 2aq The magnitudes of the electric field contributions from each charge at point P are the same. The y-components are equal, so the resultant field is...
The Electric Field due to a continuous charge distribution Divide the continuous charge distribution into a large number of small charge elements dq and calculate the (vectorial) field dE due to each (considered as a point charge). The resultant field is found by integration
The Electric Field on the axis of a charged straight rod (line of charge) There is a charge per unit length of, so dq = dx and q = l. Note y-components cancel
The Electric Field on the axis of charged ring The resultant field on axis must have no perpendicular component by symmetry. The charge element is
The cathode ray tube This device is used to display electronic information from oscilloscopes, radar systems, television receivers and computer monitors. An electron beam is produced by an electron gun, which consists of a biased hot filame