News. Charge and Potential. Charge Density. Charge and Potential Quiz #2: Monday, 3/14, 10AM Same procedure as for quiz R +

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1 News Charge and Potential Quiz #2: Monday, 3/14, 10AM Same procedure as for quiz 1 Review in class Fri, 3/11 Evening review, Fri, 3/11, 68PM 2 practice quizzes ( practice problems) Formula sheet R Charged Sphere V=1/(4! " 0 R) Q Geometry! Parallel Plate Capacitor d V= d/(a " 0 ) Q Demo: Charge Density Application: Lightning rod Biggest E near pointy tip! Local radius of curvature Charge and Potential For given geometry, Potential and Charge are proportional Define Q = C V > C is Capacitance Measured in [F] = [C/V] : Farad C tells us, how easy it is to store charge on it (V = Q/C )

2 Q Q2 Q1 Capacitance slope = C C big C small Capacitor Def: Two conductors separated by insulator Charging capacitor: take charge from one of the conductors and put on the other separate and charges V0 V C bigger > Can store more Charge! Parallel Plate Capacitor Energy stored in Capacitor Q d Q Work W = 1/2 Q 2 /C = 1/2 C V 2 needed to charge capacitor Energy conserved But power can be amplified To store lots of charge Charge slowly make A big Discharge very quickly make d small web.mit.edu/8.02x/www

3 Demo (Loud...) Where is the energy stored? C = 100µF V ab = 4000 V U = 800 J thin wire Energy is stored in Electric Field E 2 gives Energy Density: U/Volume =! e 0 E 2 Q Q d Dielectrics Dielectric Demo Parallel Plate Capacitor: C = "0 A/d Ex. A = 1m 2, d=0.1mm > C ~ 0.1µF How can one get small capacitors with big capacity? n your toolbox: 2 cm C = 1000µF Q Q Start w/ charged capacitor d big > C small > V large nsert Glass plate Now V much smaller C bigger But A and d unchanged! Glass is a Dielectric

4 Microscopic view Dielectric Constant Polarization Q P = const. E = "0 # E Q Dielectric reduces field E 0 (K > 1) E = 1/K E0 Dielectric increases Capacitance C = Q/V = Q/(E d) = K Q/(E0d) This is how to make small capacitors with large C! Electric Current We left Electrostatics Now: Charges can move in steady state Electric Current : = dq/dt Net amount of charge moving through conductor per unit time Units: [] = C/s = A (Ampere) Electric Current Current = dq/dt has a direction Convention: Direction of flow of positive charges n our circuits, carried by electrons To get a current: Need mobile charges Need E > 0 (Potential difference)

5 Demo Demo ons discharge Electroscope Charged ons Glass Light Bulb Electroscope Voltage source Molten glass: Charge carriers become mobile > Current flows > Bulb lights up! Demo Demo V Light Bulb Voltage source Light bulb (bright) Distilled Water 110 V Add NaCl: Dissociates into Na and Cl Charge carriers are available > Current flows > Bulb lights up Liquid Nitrogen (T ~ 200 o C) Wire cold > less resistance > more current > bulb burns brighter

6 Resistivity nterplay of scattering and acceleration gives an average velocity v D vd is called Drift velocity How fast do the electrons move? Thermal speed is big: v th ~ 10 6 m/s Drift velocity is small: v D ~ 10 3 m/s All electrons in conductor start to move, as soon as E> 0 Resistance Define R = V/ : Resistance R = $ L /A for constant cross section A R is measured in Ohm [%] = [V/A] Resistivity $ is property of material (e.g. glass) Resistance R is property of specific conductor, depending on material ($) and geometry Ohm s law V = R Conductor is Ohmic, if R does not depend on V, For real conductors, that is only approximately true (e.g. R = R(T) and T = T()) Approximation valid for resistors in circuits not valid for e.g. light bulbs Electric Power Use moving charges to deliver power Power = Energy/time = dwdt = (dq V)/dt = dq/dt V = V = 2 R = V 2 /R

7 Electric circuits Resistor R Capacitor C & Source of EMF Units are [V] R b c V R & & a d a b c d Electromotive Force EMF Def: & = Work/unit charge & is Electromotive Force (EMF) nternal resistance Electric Circuits Sources of EMF have internal resistance r Can t supply infinite power Battery & a R r b Vab = & r = R > = & /(rr) Resistors in series R1 R 2 Va Vb Vc Vac = V ab V ac = R 1 R 2 = (R 1 R 2 ) = R eq for R eq = (R 1 R 2 )

8 Electric Circuits Resistors in parallel R1 V a Vb R 2 = 12 = Vab/R1 Vab /R2 = Vab /Req C1 C2 Electric Circuits Two capacitors in series V 14 = V 23 V 56 Q = Q 1 = Q 2 V tot = Q 1 /C 1 Q 2 /C 2 = Q/ (C1C2) 1/Ctot = 1/C11/C2 > 1/Req = 1/R1 1/R2 nverse Capacitances add! 1 V 14 4 C C V14 Electric Circuits Two capacitors in parallel V 56 = V 23 = V 14 (after capacitor is charged) Q 1 /C 1 = Q 2 /C 2 = V 14 Qtot = Q1 Q2 Ctot = (Q1 Q2 )/ V14 = C1C2 Capacitors in parallel > Capacitances add! Demo DC Supply 9 Diode Light Bulb 4 Water cell Resistor 3 2 Fluorescent Tube? EMF & = V 12 V 34 V 56 V 78 V 910 1

9 V & Loop Rule V12 = R12 V34 = R34 V 56 = R 56 V 78 = R 78 V 910 = R n general, ' Vj= 0 Loop Rule Junction rule At junctions: ' iin = ' jout 1 Kirchoff s rules 2 2 Charge conservation Loop rule Around closed loops: ' ( Vj = 0 ( V for both EMFs and Voltagedrops Energy conservation Kirchoff s rules Kirchoff s rules allow us to calculate currents for complicated DC circuits Main difficulty: Signs! Rule for resistors: Va (V = V b V a = R, if we go in the direction of (voltage drop!) R Vb Kirchoff s rules Kirchoff s rules allow us to calculate currents for complicated DC circuits Main difficulty: Signs! Rule for EMFs: Va Vb (V = V b V a = &, if we go in the direction of

10 12V r 1% & 3% 1A r, &, 1? 3 unknowns Example 1 2A Pick signs for 1, & Junction rule 1 = 1A 2A = 3A Loop rule (1) 12V 6V 3A r = 0 > r = 6/3 % = 2 % Loop rule (2) 12V 6V 1V & = 0 > & = 5V Experiment EF MMM2 HVPS V V d MMM1 Al Foil Q = CV = "0A/d V Q Q web.mit.edu/8.02x/www