PHY 201 Chapter 21, Fall 2017

Electricity and Magnetism PHY 201 Dr. J. Romanos CHAPTER 21 Electric Charge Introduction PHY 201 Ancient Greek philosopher Thales of Miletus reported the attractive properties of amber when rubbed PHY 201 Brief History: Electric Charge Thales of Miletus 600 BC 1675 AD, Robert Boyle: Electric attraction and repulsion in vacuum 17th Century 1729 AD, Stephen Gray: Materials are classified as conductors and insulators 1733 AD, du Fay: Two distinct types of electricity 1750 AD, Benjamin Franklin: positive and negative label 1770 AD, Coulomb: Inverse Square Law 18th Century 1839 AD, Michael Faraday: Electricity with different polarities 1890 AD J.J. Thompson: Quantization of electric charge 19th Century Coulomb B. Franklin Faraday PHY 201 (a) The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other. (a) The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other. Glass rubbed with silk cloth: glass + and silk - Plastic rubbed with fur: plastic - and fur + PHY 201 Electric Charge (a) Two charged rods of the same sign repel each other. (b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge. Charging by: 1) Conduction 2) Induction 1) Charging by Conduction (contact) PHY 201 2) Charging by Induction (no contact) PHY 305  When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded  A negatively charged rubber rod is brought near a neutral sphere. The charges in the sphere are redistributed: Some of the electrons in the sphere are repelled from the electrons in the rod  The region of the sphere nearest the negatively charged rod has an excess of positive charge because of the migration of electrons away from this location.  A grounded conducting wire is connected to the sphere (Allows some of the electrons to move from the sphere to the ground)  The wire to ground is removed, the sphere is left with an excess of induced positive charge  The positive charge on the sphere is evenly distributed due to the repulsion between the positive charges PHY 201 Conductors /Insulators PHY 201 Materials classified based on their ability to move charge • Conductors are materials in which a significant number of electrons are free to move. Examples include metals. • The charged particles in nonconductors (insulators) are not free to move. There are few (if any) free electrons in a nonconductor. Examples include rubber, plastic, glass. • Semiconductors are materials that are intermediate between conductors and insulators. Examples include silicon and germanium in computer chips. • Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance. PHY 201 • Charged Particles. The properties of conductors and insulators are due to the structure and electrical nature of atoms. Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus and do not move. 𝐙 𝐀𝐗 Z: Atomic number (number of protons) N: Number of neutrons A: Mass number (A = Z + N) For neutral atoms, Z is also the number of electrons A neutral atom has equal numbers of protons and electrons. Proton Neutron PHY 201 . Proton Neutron  For conductors, outermost electrons are loosely held by nucleus  For insulators, outermost electrons are tightly held by nucleus  A neutral atom has equal numbers of protons and electrons  An atom becomes a positive ion when it loses electrons and a negative ion when it gains electrons PHY 201 • When atoms of a conductor like copper come together to form the solid, some of their outermost—and so most loosely held—electrons become free to wander about within the solid, leaving behind positively charged atoms ( positive ions). • We call the mobile electrons conduction electrons. • Only conduction electrons can move Conduction Electrons PHY 201 Charged Insulator ?! In insulator, such as glass, the atoms' electrons have very little freedom to move around. External forces such as physical rubbing can force some of these electrons to leave their respective atoms and transfer to the atoms of another material, they do not move between atoms within that material very easily. PHY 201 Induced Charge. A neutral copper rod is electrically isolated from its surroundings by being suspended on a non-conducting thread. Either end of the copper rod will be attracted by a charged rod. Here, conduction electrons in the copper rod are repelled to the far end of that rod by the negative charge on the plastic rod. Then that negative charge attracts the remaining positive charge on the near end of the copper rod, rotating the copper rod to bring that near end closer to the plastic rod. Conductor: Induced charge Insulator: Polarization  The charged object (on the left) induces charge on the surface of the insulator  A charged comb attracts bits of paper due to polarization of the paper PHY 201 PHY 201 + + Coulomb’s law PHY 201 Coulomb’s law • Charles Coulomb measured the magnitudes of electric forces between two small charged spheres • He found the force depended on the charges and the distance between them r r k q q F ˆ 2 1 2   PHY 201 The electrostatic force on particle 1 can be described in terms of a unit vector r along an axis through the two particles, radially away from particle 2. Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the particles have charges q1 and q2, are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magnitude of the force acting on each due to the other is given by where ε0 = 8.85 ×10-12 C2/N.m2 is the permittivity constant. The ratio 1/4πε0 is often replaced with the electrostatic constant (or Coulomb constant) k=8.99×109 N.m2/C2. Thus k = 1/4πε0 . Coulomb’s law PHY 201 • The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). • If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge. PHY 201 Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Charge is quantized and conserved PHY 201 Charge is Quantized • Electric charge is measured in Coulomb • The smallest charge you can find is • Electric charge is quantized (restricted to certain values). All other charges are multiple of this charge. • The charge of a particle can be written as ne, where n is a positive or negative integer and e is the elementary charge. Any positive or negative charge q that can be detected can be written as in which e, the elementary charge, has the approximate value PHY 201 Charge is Quantized  When a physical quantity such as charge can have only discrete values rather than any value, we say that the quantity is quantized.  It is possible, for example, to find a particle that has no charge at all or a charge of +10e or -6e,  Charge of 3.57e is not possible PHY 201 Charge is Conserved The net electric charge of any isolated system is always conserved. If two charged particles undergo an annihilation process, they have equal and opposite signs of charge. If two charged particles appear as a result of a pair production process, they have equal and opposite signs of charge. A photograph of trails of bubbles left in a bubble chamber by an electron and a positron. The pair of particles was produced by a gamma ray that entered the chamber directly from the bottom. Being electrically neutral, the gamma ray did not generate a telltale trail of bubbles along its path, as the electron and positron did. PHY 201 Electric Charge • The strength of a particle’s electrical interaction with objects around it depends on its electric charge, which can be either positive or negative. Conductors and Insulators • Conductors are materials in which a significant number of electrons are free to move. The charged particles in nonconductors (insulators) are not free to move. Coulomb’s Law • The magnitude of the electrical force between two charged particles is proportional to the product of their charges and inversely proportional to the square of their separation distance. • . Eq. 21-4 Eq. 21-12 Conservation of Charge • The net electric charge of any isolated system is always conserved. 21 Summary 21 Summary