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Physics 272 Electricity Magnetism Geometric Optics Spring 2015 Prof. Philip von Doetinchem [email protected] PHYS272 - Spring 15 - von Doetinchem - 67 PHYS272 - Spring 15 - von Doetinchem - 68 Electric charge ● Four different kind of forces exist: Gravitation – Electromagnetic – Weak – Strong ● ● ● We will cover electromagnetism Strength of interaction is determined by charge (similar to mass for gravity) Charges are accelerated by electric forces similar to masses in gravitational fields ● Electric currents are streams of charged particles ● Charges exert electrostatic forces on each other PHYS272 - Spring 15 - von Doetinchem - 75 Electric charge ● Important for chemistry, biology, technology ● Charges in motion: magnetism and nature of light ● Two positive charges or two negative charges repel each other. A positive charge and a negative charge attract each other. Source: http://en.wikipedia.org/wiki/Electric_charge PHYS272 - Spring 15 - von Doetinchem - 76 Electric charge and the structure of matter ● ● ● ● ● Atoms are made of protons (positive charge), neutrons, and electrons (negative charge) Attractive electric force keeps atoms together – Story more complicated: electrons have to obey Pauli principle, uncertainty relation – Nucleus bound by strong nuclear force Protons and electrons have the same absolute charge value, but the proton is ~2000x heavier Source: http://en.wikipedia.org/wiki/Atom A atom is neutral if the number of protons and electrons is the same Ion: positive: electron was removed negative: additional electrons PHYS272 - Spring 15 - von Doetinchem - 77 Electric charge is conserved ● ● The algebraic sum of all the electric charges in any closed system is constant. If an object is charged it acquires or looses negative charge → therefore it gains or loses mass ● Charge cannot be created or destroyed ● Universal conservation law ● ● The magnitude of charge of the electron or proton is a natural unit of charge. Charge can only be changed in integer numbers (quantized) PHYS272 - Spring 15 - von Doetinchem - 78 Charging https://www.youtube.com/watch?v=KtvdaeYKCLE PHYS272 - Spring 15 - von Doetinchem - 79 Charging ● ● ● ● ● Electrons have to be transferred from one object to the other A plexiglass rod rubbed with fur transfers electrons to the fur: net positive electric charge rubber rod rubbed with fur picks up a negative electric charge rods brought in contact with hanging tinsel → tinsel becomes charged and flares out → other rod will now attract the tinsel → touching the tinsel with your hand discharges it. touching a charged rod to the balloon transfers charge → balloon is repelled away from the rod PHYS272 - Spring 15 - von Doetinchem - 80 Charging Examples: – Carpet fibers on a dry day → charge builds up on you → rapid charge transfer to doorknob Likes to lose electrons your hand glass your hair nylon wool fur silk paper cotton hard rubber polyester polyvinylchloride plastic Likes to accept electrons http://phet.colorado.edu/en/simulation/travoltage PHYS272 - Spring 15 - von Doetinchem - 81 Conductors, insulators, induced charges ● ● ● Some materials are conductors of electricity, some are insulators Conductors allow charges to easily move through them Most metals: good conductors: outer electrons of atoms become detached and move freely ● Insulator: electrons are bound and cannot move ● Semiconductors have intermediate properties PHYS272 - Spring 15 - von Doetinchem - 82 Charging by induction ● ● ● Free electrons are repelled and cannot escape Negative charge on one site, positive charge on the other: induced charge Forces reach equilibrium PHYS272 - Spring 15 - von Doetinchem - 83 Electric forces on uncharged objects http://www.youtube.com/watch?v=TE2r0vjkXK0 PHYS272 - Spring 15 - von Doetinchem - 84 Charging by induction https://phet.colorado.edu/en/simulation/balloons PHYS272 - Spring 15 - von Doetinchem - 85 Electric forces on uncharged objects ● ● ● A charged body can exert forces on uncharged objects Charge-induced effect Charged balloon causes slight shifting of charge in the ceiling PHYS272 - Spring 15 - von Doetinchem - 86 ● ● ● If the distance between two charged objects is much larger than their dimension → charges can be treated as point charge Strength of electric force is proportional to 1/r2 Source: http://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb Coulomb's law Charles-Augustin de Coulomb (1736-1806) The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. PHYS272 - Spring 15 - von Doetinchem - 88 Coulomb's law https://www.youtube.com/watch?v=B5LVoU_a08c PHYS272 - Spring 15 - von Doetinchem - 89 Coulomb's law ● Force magnitude is always positive ● Direction is always along the line of the two charges ● ● ● If both charges are positive: repulsive If both charges are negative: repulsive If have charges have opposite charge signs: attractive Newton's third law is valid for charges: actio est reactio Form of force is similar to gravity, but two different types of forces (gravity is never repulsive) PHYS272 - Spring 15 - von Doetinchem - 90 Fundamental electric constants ● constant k depends on the system of units, in SI (Système international d’unités) units: ● Electric current: charge per second: Ampere ● To make things easier for the following: PHYS272 - Spring 15 - von Doetinchem - 91 Fundamental electric constants ● Natural unit of charge for proton and electron: ● Charge of 1 electron: -e ● Charge of 1 proton: +e ● Typical charges are 10-9C to 10-6C (1nC to 1C) PHYS272 - Spring 15 - von Doetinchem - 92 Coulomb's law with vectors absolute charge values distance between charges positive or negative direction comes from product of q1 and q2 unit vector along the direct connection between charges q1 and q2 → do not confuse the actual vector and the unit vector of PHYS272 - Spring 15 - von Doetinchem - 93 Coulomb's law http://employees.oneonta.edu/viningwj/sims/coulombs_law_s.html PHYS272 - Spring 15 - von Doetinchem - 94 Superposition of forces ● Total force is the vector sum of forces: principle of superposition of forces: PHYS272 - Spring 15 - von Doetinchem - 95 Electric field and electric forces ● ● ● How do electric charges know of each others existence? What is an electric field? A single charge causes an electric field in the surrounding space If you drop a second charge in this field the two charges communicate through their fields PHYS272 - Spring 15 - von Doetinchem - 98 Electric field and electric forces ● ● The fields are responsible for exerting the electric force on the other charge An electric field creates an electric force on a test charge q0 PHYS272 - Spring 15 - von Doetinchem - 99 Electric field and electric forces ● ● ● The electric field concept is again analogous to the gravitational field Electrical field is useful because it does not depend on the charge of the body on which the electric force is exerted. Calculation of electric field becomes more complicated if the charged object is not point like. Field strength and direction will depend on the relative position to the object. PHYS272 - Spring 15 - von Doetinchem - 100