Chapter 23 Electric Fields Summer 1996, Near the University of Arizona

Electricity and Magnetism, Some History Chinese Documents suggest that magnetism was observed as early as 2000 BC Greeks Electrical and magnetic phenomena as early as 700 BC Experiments with amber and magnetite

Electricity and Magnetism, Some History, William Gilbert showed electrification effects were not confined to just amber The electrification effects were a general phenomena 1785 Charles Coulomb confirmed inverse square law form for electric forces

Electricity and Magnetism, Some History, Hans Oersted found a compass needle deflected when near a wire carrying an electric current 1831 Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire

Electricity and Magnetism, Some History, James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism Unified electricity and magnetism 1888 Heinrich Hertz verified Maxwell’s predictions He produced electromagnetic waves

PHYS202 in 5 equations     

Electric Charges, 1 There are two kinds of electric charges Called positive and negative Negative charges are the type possessed by electrons Positive charges are the type possessed by protons Like charges repel Unlike charges attract

Electric Charges, 2 The rubber rod is negatively charged The glass rod is positively charged The two rods will attract

Electric Charges, 3 The rubber rod is negatively charged The second rubber rod is also negatively charged The two rods will attract

Conservation of Electric Charges A glass rod is rubbed with silk Electrons are transferred from the glass to the silk Each electron adds a negative charge to the silk An equal positive charge is left on the rod

Quantization of Electric Charges The electric charge, q, is said to be quantized q is the standard symbol used for charge as a variable Electric charge exists as discrete packets q = Ne N is an integer e is the fundamental unit of charge |e| = 1.6 x C Electrons: q = -e Missing Electrons: q = +e

Conductors Electrical conductors are materials in which some of the electrons are not bound to atoms These electrons can move relatively freely through the material Examples of good conductors include copper, aluminum and silver When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

Insulators Electrical insulators are materials in which all of the electrons are bound to atoms These electrons cannot move relatively freely through the material Examples of good insulators include glass, rubber and wood When a good insulator is charged in a small region, the charge is unable to move to other regions of the material

Semiconductors The electrical properties of semiconductors are somewhere between those of insulators and conductors Examples of semiconductor materials include silicon and germanium

Charging by Induction Charging by induction requires no contact with the object inducing the charge Assume we start with a neutral metallic sphere The sphere has the same number of positive and negative charges

Charging by Induction, 2 A charged rubber rod is placed near the sphere It does not touch the sphere The electrons in the neutral sphere are redistributed

Charging by Induction, 3 The sphere is grounded Some electrons can leave the sphere through the ground wire

Charging by Induction, 4 The ground wire is removed There will now be more positive charges The positive charge has been induced in the sphere

Charging by Induction, 5 The rod is removed The electrons remaining on the sphere redistribute themselves There is still a net positive charge on the sphere

Coulomb’s Law The electrical force between two stationary charged particles is given by Coulomb’s Law The force is inversely proportional to the square of the separation r between the particles and directed along the line joining them The force is proportional to the product of the charges, q 1 and q 2, on the two particles

Coulomb’s Law, 2 The force is attractive if the charges are of opposite sign The force is repulsive if the charges are of like sign The force is a conservative force

Point Charge The term point charge refers to a particle of zero size that carries an electric charge The electrical behavior of electrons and protons is well described by modeling them as point charges

Coulomb’s Law, Equation Mathematically, The SI unit of charge is the coulomb (C) k e is called the Coulomb constant k e = x 10 9 N. m 2 /C 2 = 1/(4πe o ) e o is the permittivity of free space e o = x C 2 / N. m 2

Coulomb's Law, Notes Remember the charges need to be in coulombs e is the smallest unit of charge except quarks e = 1.6 x C So 1 C needs 6.24 x electrons or protons Typical charges can be in the µC range Remember that force is a vector quantity

Vector Nature of Electric Forces In vector form, is a unit vector directed from q 1 to q 2 The like charges produce a repulsive force between them

Vector Nature of Electrical Forces, 2 Electrical forces obey Newton’s Third Law The force on q 1 is equal in magnitude and opposite in direction to the force on q 2 F 21 = -F 12 With like signs for the charges, the product q 1 q 2 is positive and the force is repulsive

Superposition Principle, Example The force exerted by q 1 on q 3 is F 13 The force exerted by q 2 on q 3 is F 23 The resultant force exerted on q 3 is the vector sum of F 13 and F 23

Three point charges are located at the corners of an equilateral triangle as shown in the figure (q = 2.50 µC, L = m). Calculate the resultant electric force on the 7.00 µC charge. Problem

Zero Resultant Force, Example Where is the resultant force equal to zero?