Phy 203: General Physics III

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

2. 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 (qproton = +1.602x10-19 C) • Negative (-): e.g. electrons (qelectron = -1.602x10-19 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 1.602x10-19 C • The net charge of any matter is qnet = Ne • Electric charge is conserved • There is no known process that can change the charge of something

3. 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 109 N.m2/C2{Coulomb’s constant} r is the separation distance between charges q1 & q2 are the magnitude of charges respectively • The direction of FE is determined by the sign of the charges

4. Charles Augustin de Coulomb(1736-1806) • 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 1785-1791), including: • The law of attraction and repulsion • The electric point charges • Magnetic poles • The distribution of electricity on the surface of charged bodies

5. - + 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

6. The Electric Field (cont.) • The magnitude of electric field for a point charge (q): • The force (FE) acting on a “test” charge (qo) placed in an electric field (E) is FE = qoE • Note the similarity of the electric force law to Newton’s 2nd 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 = FE/qo

7. A A + + + + - - - - +q -q E Parallel Plate Capacitor A is surface area q is charge on each face E is electric field • 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/eoA = s/eo(for air filled capacitor) where eo is 8.85 x 10-12 C2/(N.m2), the permittivity constant (free space) and s is the surface charge density (q/A)

8. 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

9. Electric Shielding • As stated previously, the electric field inside a conducting material is zero (Einside=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

10. 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 .cosf) and surface area (A) or FE= (E .cosf).A {electric flux} Gauss’ Law: • The total electric flux through any closed (“Gaussian”) surface is equal to the enclosed charge (Qenclosed) divided by the permittivity of free space (eo) FE= S (E .cosf).A = Qenclosed/ eo • Gauss’ Law can be used to determine the electric field (E) for many physical orientations (distributions) of charge

11. Johann Carl Friedrich Gauss(1777-1855) • 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??)