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Transcript
Lecture 1 Introduction Electricity and Magnetism are all around us. Not only in the devices we use every day (cell phones, computers etc.) but almost everything we see happening around us is due to electricity and magnetism. For example: Atoms and molecules are held together by electric forces and therefore chemical reactions occur because of electric forces Light is an electromagnetic wave, so we learn about the world also using electric forces. Atoms in solids are also held together by electric forces. In fact the only other force we experience is gravity. Everything else is electricity and magnetism. • In physics we learn by measuring. The most basic measurement: SIZE • Why? Because objects behave differently at different scales, the forces that act are different. Quantum Mechanics Electricity and Magnetism Nuclear Radioactivity Newtonian/Einstein Dark Matter (83%!!) and Dark Energy Gravity Aside: Prefixes and notations for large and small quantities Factor prefix Abbr. 10-15 femto f 10-12 pico p 10-9 nano n 10-6 micro m 10-3 milli m 103 kilo K 106 mega M 109 giga G 1012 tera T 1 Gravity • Law of Gravity: (Newton) Two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of their distances. Greatest achievement? Discovering the law of gravity is possibly one of the greatest achievements of humankind. What do you think? A. B. C. D. Going to the Moon Invention of computers Mapping of DNA Other Problem Using that (these are approximate numbers) • the radius of the Earth is 6000Km • the acceleration of gravity on the surface is 10 m/s2 • the density of the Earth is five times that of water • Estimate the value of Newton’s constant G Problem Using that the period of the Moon is approximately one month, estimate the distance from the Earth to the Moon. How can you use that to know the size of the Moon? HOw can you use that to estimate the time it takes a rocket to reach the Moon? Lecture 2 Review question What’s the size of an atom? A. B. C. D. 10-15 m 10-10 m 10-3 m 1m Lecture 2 Electrostatics: Charge and fields Electrostatics describes the interactions of electric charges in the same way that gravity describes the interactions of masses. It follows Coulomb’s law: Crucial difference: The force can be attractive or repulsive. 1. Charges of the same sign repel each other. Of opposite sign attract each other. 2. Charges add up with sign. So, two charges of opposite sign and equal magnitude cancel each other producing a neutral object which feels no electric force. 3. Charge is conserved, it cannot be created or destroyed. 4. C means Coulomb, unit of electric charge. Some considerations: • Why statics? If charges move, they create also magnetic fields, that are important if the charges move close to the speed of light, or we have many charges moving together (electric current). Is there a similar effect in gravity? • Minimal electric charge: Electron: • The charge of the proton has the same value but opposite sign. Why? • Atoms are exactly neutral, however there are residual forces. • These residual forces are responsible for most phenomena we see in Nature. There are exceptions, for example lightning. • On the other hand we have learned to use special materials like metals, insulators, semiconductors, superconductors, etc. to use electric (and magnetic) forces to our advantage. Conductors and insulators • Conductors allow charges to move freely inside them. • Insulators can be charged by friction for example, but charges stay fixed in the same place. • Since charges of the same sign repel each other, in a conductor charges migrate to the surface. • We can charge a conductor using an interesting phenomenon called induction. Q=0 Charged insulator Total charge is CONSERVED. Therefore the conductor acquires no charge. What to do? We need to bring charge from somewhere else!. Connections to ground: an infinite reservoir of charge. Connecting circuits to ground makes them more stable and safe. It should always be done when possible. Electric field Electricity is not just forces between charges. Light and radio waves are examples of how electric phenomena can propagate and exist independently of charges. The electric field is a vector and can be detected by putting a test charge which will feel a force: Principle of superposition: Electric fields from different sources add up as vectors. This implies the principle of superposition for forces: Clicker question Given the formula , in which units is the Electric Field measured? 1. 2. 3. 4. N (Newtons) N/C (Newtons / Coulomb) N C (Newtons . Coulombs) V/m (Volts / meters) • Addition of vectors Simple example: displacements. We move 30m to the North, then 20 meters East and then 10m SW: 1 1 (0,30) (20,0) 10( , ) 2 2 10 10 (20 ,30 ) 2 2 (12.93,22.93) tan 22.93 12.93 L 12.932 22.932 Lecture 3 Review question Besides the Coulomb law, other effects appear if: A. B. C. D. Charges are very large. Charges are moving fast. Charges are very far away from each other. Charges are very close to each other. Lecture 3 Electrostatics: Electric field / Energy The Electric field is a vector field. It defines a vector at each point in space. Drawing an arrow at (a few) points in space is one option to represent vector fields graphically. Another is to draw lines which, at each point are parallel to the electric field. They area called “lines of electric field” Vector fields are everywhere. Example, motion of air, the velocity is a vector field. The lines are now lines of flow which indicate how air moves. Electric field of a spherical charge Electric field is measured in N/C Dipole: Two charges of equal absolute value but opposite sign. Lines of electric field start from positive charges and end in negative charges Generating electricity: Kelvin generator Clicker question Where is the energy to light the bulbs coming from? A. B. C. D. Hidden battery Friction Water Gravity Hint: When will it stop working? and what do you have to do to make it work again? Energy is always conserved! You can convert one type of energy into another: Wind Gravity electricity (wind mill) electricity (hydroelectric dam) Don’t confuse Energy with Power. Power is Energy produced (or consumed) per unit time. Units of Energy: J (Joules) = N m = Kg m2/s2 Units of Power: W (Watts) = J/s In Newtonian mechanics, forces can be derived from potentials electrostatic potential Work: [ If there is an angle between force and displacement, we multiply by the cosine of the angle ] To reproduce Coulomb’s law we need • Proposal: • Verification: We need to use: as we wanted!. to get Lecture 4 Electrostatic potential In the same way we defined Electric field from the force we define electrostatic potential from the potential energy. units: V (Volt) For a charged particle (or a charged sphere): The potential decreases along the lines of electric field. V1 E V2 V1>V2 Clicker question Electrostatic potential is measured in Volts which, in view of the formula , is the same as: A. B. C. D. N/C N m /C NC/m Nm2 /C Hint: Remember U is energy, same units as work W = F Dx Some comments • Principle of superposition: V = V1 + … + Vn as scalars (numbers) • Constant electric field • Equipotential surfaces: Surfaces of constant potential. Perpendicular to the electric field. E.g. the surface of a conductor (static case). Potential of a spherical conductor For a point charge we said: Equipotential surfaces are concentric spheres. (V is constant if r is constant) If it is a charged sphere, then the potential outside is the same If it is a conductor there is no electric field inside (in the static case) and therefore inside the potential is constant (no work needed to move a probe charge). In pictures: E(r) Notice V is continuous but E can jump An interesting problem: Two conducting spheres of different radii are charged and in contact. Which one has the largest charge?. Solution: The spheres are in contact so they form a single conductor, the potential has to be the same: Therefore (V1=V2) Notice the electric field So: If one sphere is very small the electric field is huge!! Lightning rod. We said many times that the potential inside a conductor is constant, no electric field. This is true even is there is hole in it (with no charge). Therefore conductors can act as shields. This is known as Faraday cage and it is extremely important in applications. For example to insulate delicate electronic devices. Or for “secrecy”, stopping cell phones, etc. Electric flux An important idea in physics (and science) is to use analogous concepts to describe different phenomena. Example: vector field. When a vector field represent motion of air an important concept is that of flow, how much air goes through a surface. It is given by: If we replace velocity by electric field we obtain the Electric Flux through a surface. It is easiest to compute if the surface is everywhere perpendicular to the field. Equipotentials! Case of sphere Gauss law: Total electric flux through a closed surface is equal to the total charge enclosed by the surface divided by e0 Further check, consider a truncated cone, the flux is the same but opposite on the two “lids”. Therefore the total flux is zero. OK, no charge inside! Application: Field of a charged plane with charge density s (Q= sA). Useful later for capacitors.