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Electric Forces Coulomb’S Law College Physics B Electric Forces Coulomb’s Law Motion of Electric College Physics B - PHY2054C Charge Conductors Insulators Metals Static Electricity Electric Forces and Fields Electric Field Electric Flux Gauss’ Law 08/27/2014 My Office Hours: Tuesday 10:00 - 12:00 Noon 206 Keen Building College Physics B Outline Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field Electric Flux Insulators Gauss’ Law Metals Static Electricity 3 Electric Field 4 Electric Flux Gauss’ Law College Physics B Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Discovery of electricity is generally credited to the Greeks. Electric Flux Gauss’ Law • About 2500 years ago: They observed electric charges and the forces between them in many situations. • Greeks used amber (a type of dried, hardened tree sap) and rubbed it with a piece of animal fur. ➜ Greek word for amber was electron. • The observed force even occurs when the amber (or plastic in the picture) and the paper are not in contact. College Physics B Electric Forces Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law College Physics B Electric Forces Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge • Conductors Assume two charged particles can be modeled Insulators Metals as point particles. Static Electricity Electric Field Electric Flux Gauss’ Law College Physics B Electric Forces Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge • Conductors The magnitude of the electric force between the Insulators Metals two particles is given by Coulomb’s Law. Static Electricity Electric Field Electric Flux Direction of the force is along the Gauss’ Law line that connects the 2 charges. • A repulsive force will give a positive value for F. • An attractive force will give a negative value for F. • k = 8.99 × 109 N · m2/C2 “Coulomb constant” College Physics B Features of Coulomb’s Law Electric Forces Coulomb’s Law Direction of the force Motion of • The product q · q determines the sign. Electric 1 2 Charge • Conductors For like charges, the product is positive. Insulators ➜ Metals The force tends to push the charges farther Static Electricity apart. Electric Field • Electric Flux For unlike charges, the product is negative. Gauss’ Law ➜ The charges are attracted to each other. College Physics B Features of Coulomb’s Law Electric Forces Coulomb’s Law Direction of the force Motion of • The product q · q determines the sign. Electric 1 2 Charge • Conductors For like charges, the product is positive. Insulators ➜ Metals The force tends to push the charges farther Static Electricity apart. Electric Field • Electric Flux For unlike charges, the product is negative. Gauss’ Law ➜ The charges are attracted to each other. The form of Coulomb’s Law is similar to Newton’s Law of Universal Gravitation: q ·q · 1 2 F G m1 m2 F = k r 2 = r 2 r = distance between q1 and q2 or m1 and m2 attractive or repulsive always attractive! College Physics B Gravity Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law “Inverse-Square Law” College Physics B Gravity Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law “Inverse-Square Law” College Physics B Coulomb’s Law Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law Every charged particle in the universe attracts (or repels) every other charged particle with a force that is directly proportional to the product of the charges of the particles and inversely proportional to the square of the distance between them. Electric Field Hockey: phet.colorado.edu/en/simulation/electric-hockey College Physics B Coulomb’s Law Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Charles-Augustin de Coulomb Electric Flux (14 June 1736 - 23 August 1806) Gauss’ Law q q F = k 1 2 r 2 1 k = = 8.99 × 109 N · m2/C2 4πǫ0 ǫ0 is called permittivity of free space College Physics B Example: Hydrogen Atom Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law q · q −(1.6 × 10−19)2 F = k · proton electron = 8.99 × 109 · N r 2 (0.53 · 10−10)2 ≈− 8.2 × 10−8 N a = F/m ≈ 9.0 × 1022 m/s2 with r = 0.53−10 m. College Physics B Example: Helium Nucleus Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law q · q (1.6 × 10−19)2 F = k · proton proton = 8.99 × 109 · N r 2 (10−15)2 ≈ + 230 N with r = 10−15 m. College Physics B Size of the Electric Force Electric Forces Coulomb’s Law Motion of Assume you have two boxes each containing 1 g of Electric Charge electrons: Conductors Insulators • × 27 Metals There would be 1.1 10 electrons in each box. Static Electricity • Electric Field The force between the two boxes would be about × 26 Electric Flux 3 10 N with the boxes separated by r = 1 m. Gauss’ Law ➜ This is almost a million times larger than the force between the Sun and the Earth. College Physics B Superposition of Forces Electric Forces Coulomb’s Law Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Electric Flux Gauss’ Law When there are more than two charges in a problem, the “Superposition Principle” must be used. 1 Find the forces on the charge of interest due to all the other forces. 2 Add the forces as vectors. F~ = F~1 + F~2 College Physics B Question Electric Forces Two uniformly charged spheres are firmly fastened to Coulomb’s Law Motion of and electrically insulated from frictionless pucks on an Electric Charge air table. The charge on sphere 2 is three times the Conductors Insulators charge on sphere 1. Which force diagram correctly Metals Static Electricity shows the magnitude and direction of the electrostatic Electric Field forces? Electric Flux Gauss’ Law A C B D College Physics B 1 Recognize the Principle • The electric force can be found using Coulomb’s Law. • Electric The principle of superposition may also be needed. Forces Coulomb’s Law 2 Sketch the Problem Motion of • Construct a drawing and show the location and charge of Electric Charge each object (include a coordinate system). Conductors • Insulators Include the directions of all electric forces acting on the Metals particle of interest. Static Electricity Electric Field 3 Identify the Relationships Electric Flux • Use Coulomb’s Law to find the magnitude of the forces Gauss’ Law acting on the particle of interest. 4 Solve • The total force on a particle is the sum of all the forces. • Add the forces as vectors. • It is usually easier to work in terms of the components along the coordinate system. 5 Check • Consider what the answer means. • Check if the answer makes sense. College Physics B Outline Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field Electric Flux Insulators Gauss’ Law Metals Static Electricity 3 Electric Field 4 Electric Flux Gauss’ Law College Physics B Structure of Matter Electric Forces Coulomb’s Law ... from an “electrical” point of view: Motion of Electric • Conductors (copper, silver, gold, iron, lead, etc.) Charge Conductors are materials, in which electric charge can move freely. Insulators Metals • Insulators (glass, plastic, rubber, wood, etc.) Static Electricity Electric Field do not allow charges to move. Electric Flux • Semiconductors (silicon, germanium, etc.) Gauss’ Law are materials, in which charges can move under the influence of small electrical forces. College Physics B Conductors Electric Forces • Each atom by itself is Coulomb’s Law Motion of electrically neutral. Electric ➜ Charge Equal numbers of Conductors Insulators protons and electrons Metals • Static Electricity When these atoms come Electric Field together to form the metal Electric Flux piece, electrons are freed. Gauss’ Law • The electrons move freely through the entire piece of metal leaving behind protons. ➜ Conduction Electrons A piece of metal can also accept extra electrons or release some of its conduction electrons so that the entire object can acquire a net positive or negative charge. College Physics B Insulators Electric Forces • In insulators, the electrons Coulomb’s Law Motion of are not able to move freely Electric Charge through the material. Conductors • Insulators Examples include quartz, Metals Static Electricity plastic, and amber. Electric Field • Electrons cannot escape Electric Flux Gauss’ Law from these ions. • There are no conduction electrons available to carry charge through the solid. • If extra electrons are placed on an insulator, they tend to stay in that same place. College Physics B Excess Charge on a Metal Electric Forces Coulomb’s Law • Electrons can move easily Motion of through a metal. Electric Charge • Conductors Excess electrons will be Insulators Metals distributed on the surface of Static Electricity the metal. Electric Field Electric Flux Why? Gauss’ Law College Physics B Excess Charge on a Metal Electric Forces Coulomb’s Law • Electrons can move easily Motion of through a metal. Electric Charge • Conductors Excess electrons will be Insulators Metals distributed on the surface of Static Electricity the metal.
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