Phy 203: General Physics III Ch 18: Electric Forces & Electric Fields Lecture Notes

Electric Charge A fundamental property of protons & electrons The SI unit of charge is the coulomb (C) Two types of charge (q): –Positive (+): e.g. protons (q proton = x C) –Negative (-): e.g. electrons (q electron = x C) Atoms & molecules have no net charge –Equal # of protons & electrons –protons & electrons have the same magnitude but opposite charge Properties of charge: –Like charges repel each other –Unlike charges attract each other Electric charge is quantized –The smallest unit of charge (e) is 1.602x C –The net charge of any matter is q net = Ne Electric charge is conserved –There is no known process that can change the charge of something

Coulomb’s Law The attractive/repulsive force between charges is called electric force (remember forces are vectors!) The magnitude of the electric force between 2 charges can be determined by Coulomb’s Law: where: k is 8.99 x 10 9 N. m 2 /C 2 {Coulomb’s constant} r is the separation distance between charges q 1 & q 2 are the magnitude of charges respectively The direction of F E is determined by the sign of the charges

Charles Augustin de Coulomb ( ) Engineer by education Won prize for his work on the subject of friction Won prize for using calculus of variations to solve engineering problems Published 7 important papers on electricity & magnetism ( between ), including: –The law of attraction and repulsion –The electric point charges –Magnetic poles –The distribution of electricity on the surface of charged bodies

The Electric Field The ability of a charge to influence other charges in its vicinity its electric field The SI units for electric field are N/C The electric field is a vector property –E fields due to multiple charges add as vectors –E field lines originate at + charges & terminate at - charges The direction of an electric field vector (at a point in space) is the direction of electric force that would be exerted by on a positive charge at that location - +

The Electric Field (cont.) The magnitude of electric field for a point charge (q): The force (F E ) acting on a “test” charge (q o ) placed in an electric field (E) is F E = q o E Note the similarity of the electric force law to Newton’s 2 nd Law (F=ma) Formal definition of electric field: –the electric force per unit charge that acts on a test charge at a point in space or E = F E /q o

Parallel Plate Capacitor A parallel plate capacitor consists of 2 conducting plates separated by a small space (which may be filled with air or some other dielectric material) Excess charge (-q) on one inner face repels equal charge away from the opposite face leaving (+q) –Charge on each face is uniformly spread out on the surface Electric field is constant between the plates –Electric field lines point from +q to -q The electric field (magnitude) inside a parallel plate capacitor is E = q/  o A =  /  o (for air filled capacitor) where  o is 8.85 x C 2 /(N. m 2 ), the permittivity constant (free space) and  is the surface charge density (q/A) A is surface area q is charge on each face E is electric field E AA +q-q

Conductors & Insulators Conductors are materials that allow electric charge to flow (or move through it) –Excess charge will repel itself pushing all excess charge to the surface of the conductor –Under equilibrium conditions, all excess charge resides along the surface of the conductor –When electric charge flows along a conductor (i.e. electricity) it flows along the surface (think about the implications!) –Electric field inside a conductor is zero Insulators are materials that do not allow electric charge to flow –Excess charge will remain fixed (or static) –Excess charge can be inside an insulator or along its surface and does not have to be uniformly distributed –Electric charge inside insulator depends on orientation and quantity of excess charge

Electric Shielding As stated previously, the electric field inside a conducting material is zero (E inside =0) If a conductor completely surrounds an empty space, the electric field inside the empty space is also zero –The conductor “shields” any charge inside region from electric fields produced outside the conductor

Gauss’ Law Gauss’ Law is a fundamental law of nature relating electric charge to electric flux Consider a electric field passing through a region in space. Electric flux is the product of electric field normal to the area (E. cos  ) and surface area (A) or  E = (E. cos  ). A {electric flux} Gauss’ Law: The total electric flux through any closed (“Gaussian”) surface is equal to the enclosed charge (Q enclosed ) divided by the permittivity of free space (  o )  E =  (E. cos  ). A = Q enclosed /  o Gauss’ Law can be used to determine the electric field (E) for many physical orientations (distributions) of charge

Johann Carl Friedrich Gauss ( ) One of the greatest mathematicians in history Published major works in the fields of: –Non-euclidian & differential geometry –Statistics (including least squares method) –Potential Theory (hence the term “potential” energy & electric potential) –Terrestrial magnetism (including least squares method) Made a fortune investing in bonds (is it just me or does Gauss look strikingly similar to Ebenezer Scrooge??)