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Physics 272 February 24 Spring 2015 www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm go.hawaii.edu/KO Prof. Philip von Doetinchem [email protected] PHYS272 - Spring 15 - von Doetinchem - 1 Kirchhoff's rules ● Kirchhoff's junction rule: Algebraic sum of currents is zero at any junction. Conservation of charge ● ● Algebraic sum of potential differences is zero in any loop. Electrostatic force is conservative. Path does not matter → potential energy is the same after going around a loop PHYS272 - Spring 15 - von Doetinchem - 2 Charging a battery - PHYS272 - Spring 15 - von Doetinchem - 3 Ammeter ● Measure current that path through the meter ● Good Ammeter has a small internal resistance pointer moves because of magnetic field interactions with electric current circuit element full scale current PHYS272 - Spring 15 - von Doetinchem - 4 Voltmeters ● ● Voltmeters should have a large resistance such that connecting them in parallel is not altering the current of the circuit Ammeter and Voltmeter in combination can measure resistance and power PHYS272 - Spring 15 - von Doetinchem - 5 R-C circuits ● ● ● ● So far: constant emfs and constant current Next steps: time dependent potentials, currents, and powers What happens when you charge a capacitor? many devices use charging and discharging constantly: – Flashing traffic lights – Car turn signals – Flash units PHYS272 - Spring 15 - von Doetinchem - 8 Charging a capacitor ● Ideal battery (zero internal resistance) ● Capacitor initially uncharged ● Close switch → charge capacitor ● Assume: ● – current starts at the same time everywhere in the circuit – Current is the same everywhere for a particular moment in time Lower case quantities are time dependent quantities in the following calculations PHYS272 - Spring 15 - von Doetinchem - 9 Charging a capacitor ● Capacitor charges: – vbc increases (charge builds up) – vab decreases (Kirchhoff's loop rule) – Current decreases (Ohm's law) PHYS272 - Spring 15 - von Doetinchem - 10 Charging a capacitor ● Eventually: – Capacitor fully charged – Current stops flowing PHYS272 - Spring 15 - von Doetinchem - 11 Charging a capacitor ● Charge at any time t during the charging process: PHYS272 - Spring 15 - von Doetinchem - 12 Charging a capacitor PHYS272 - Spring 15 - von Doetinchem - 13 Current and time constant ● time constant: =RC ● small: capacitor charges quickly ● large: capacitor charges slowly ● Charge and current processes happen on the same time scale PHYS272 - Spring 15 - von Doetinchem - 14 Charging a capacitor Charge build-up Current drop q/Qf i/I0 t t i/I0 Slope is -1/(RC) → measure properties Logarithmic plot t PHYS272 - Spring 15 - von Doetinchem - 15 Power approach ● Energy conservation: -Ri2 ● Half of the energy is stored in capacitor Other half is dissipated in resistor (does not depend on C, R, ) PHYS272 - Spring 15 - von Doetinchem - 16 Discharging a capacitor ● Remove battery ● Time constant RC stays the same ● Charge goes exponentially to zero PHYS272 - Spring 15 - von Doetinchem - 17 Example For a charging capacitor, the ratio of charge to final charge on the capacitor and the ratio of current to the initial current add up to 1. PHYS272 - Spring 15 - von Doetinchem - 18 Power distribution systems ● ● ● ● Appliances at home are always operated in parallel to the power source Modern houses have two lines with opposite polarity coming in (hot lines) A third line is grounded and provides the neutral potential Maximum current is limited by resistance of the wires (RI2 power loss) – 12 gauge wire (2.05mm → safe for 20A without overheating) – Thicker wires for, e.g.,main power lines, dryers PHYS272 - Spring 15 - von Doetinchem - 21 Circuit overloads and short circuits ● ● Overload/overheat protection is provided by fuses Fuses are designed to break circuits depending on the maximum load allowed on the wires ● Installed on hot side of incoming line ● Fuse examples: ● ● – lead-tin alloy with low melting temperature → melts when too hot → breaks circuit (one-time use) – Electromagnet or bimetallic strip interrupts circuit (can be reset) Short circuit: neutral and hot side are in contact → large current can melt wires! 3 prong connectors connect, e.g., metal housing to ground line and can prevent shocks PHYS272 - Spring 15 - von Doetinchem - 22 Where we stand Electric charges are sources of electric fields 0 (constant time, conservative electric force) PHYS272 - Spring 15 - von Doetinchem - 23 Measuring magnetic fields with test charges http://www.youtube.com/watch?v=YbzBTdU7iRU ● ● Measure deflection of moving charges in the presence of a magnetic field Example: – old televisions contained an electron beam in a cathode-ray tube – Velocity is known – If beam and magnetic field (anti)parallel → no force → no deflection – If beam and magnetic perpendicular → maximum deflection PHYS272 - Spring 15 - von Doetinchem - 24 Magnetism ● ● ● ● ● Examples: permanent magnets, compass in earth electric field Magnetic forces arise from moving electric charges Electric charges react to magnetic field Source: http://de.wikipedia.org/wiki/Magnet First: focus on how electric charges react to magnetic fields Permanent magnets: – Exert forces on each other – Exert forces on unmagnetized objects containing iron PHYS272 - Spring 15 - von Doetinchem - 25 Magnetic poles vs. electric charge ● ● ● Initially: magnets described in terms of poles – North: bar shaped magnetic material (free to rotate) points North – South: bar shaped magnetic material (free to rotate) points South – North and South attract each other – North-North and South-South repels each other Objects containing iron are attracted by South and North poles Earth is a magnet: – geographic poles close to magnetic poles: not totally parallel – Magnetic axis moves PHYS272 - Spring 15 - von Doetinchem - 26 Magnetic poles vs. electric charge ● ● ● ● ● Important: no isolated magnetic North and South poles exist Major difference to positive and negative electric charges Ørsted found that a compass needle was deflected by a current carrying wire Hans Christian Ørsted 1777-1851 Magnetic forces are due to interactions of moving electrons in atoms Source: http://de.wikipedia.org/wiki/Hans_Christian_%C3%98rsted ● Magnetized objects have coordinated motion of certain atomic electrons Unmagnetized objects do not have such a coordinated motion PHYS272 - Spring 15 - von Doetinchem - 27 Magnetic field ● ● ● ● ● A moving charge or a current creates a magnetic field in the surrounding space (in addition to electric field) The magnetic field exerts a force on any other moving charge or current that is present in the field. For now: don't worry about how exactly magnetic field is created. Magnetic field is a vector field: a vector associated with each point in space. Direction towards the north pole of a compass needle. PHYS272 - Spring 15 - von Doetinchem - 28 Magnetic forces on moving charges ● ● ● ● Magnitude of the force is proportional to amount of charge Magnitude of the force is proportional to the magnetic field strength. Magnitude of the force is proportional to the velocity – electric force is always the same: no matter if charge moves or not! – Particle at rest does not feel magnetic force Force is perpendicular to the velocity and magnetic field PHYS272 - Spring 15 - von Doetinchem - 29 Magnetic forces on moving charges Right hand rule ● Charges of same amount, but opposite sign → feel force of same magnitude, but opposite direction Force (direction of deflection) magnetic field B velocity v PHYS272 - Spring 15 - von Doetinchem - 30 Magnetic forces on moving charges ● Magnetic field of the earth: 0.1mT ● Magnetic field in atoms: 10T ● Largest magnetic field in lab: 45T ● Pulse magnetic fields produce up to: 120T ● Magnetic field and electric field: PHYS272 - Spring 15 - von Doetinchem - 31 The World's Strongest Magnet http://www.youtube.com/watch?v=6wH1kq7gfuU PHYS272 - Spring 15 - von Doetinchem - 32 Additional material PHYS272 - Spring 15 - von Doetinchem - 33 A complex network PHYS272 - Spring 15 - von Doetinchem - 34 Magnetism http://www.youtube.com/watch?v=jq8WOUFeCcg PHYS272 - Spring 15 - von Doetinchem - 35