Electric Fields I: Charge, Conductors, Coulomb's Law, and Electric Field Lines, Slides of Law

Download Electric Fields I: Charge, Conductors, Coulomb's Law, and Electric Field Lines and more Slides Law in PDF only on Docsity! Chapter 21 The Electric Field I MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 2 The Electric Field I • Charge • Conductors & Insulators • Coulomb’s Law • The Electric Field • Electric Field Lines • Action of the Electric Field on Charges MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 5 The Electron Charge of electron: -1.602 x 10-19 Coulombs The symbol e represents the value 1.602 x 10-19 Coulombs. Therefore the charge of the electron is -e The charge is quantized - all charged objects contain an integral multiple of e. Proton charge = +e The exact balancing of the protonic and electronic charges allows atoms to be effectively neutral. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 6 Electrical Phenomena Lightning Static electricity Triboelectricity - charging by friction - unbalancing the neutral atoms. Triboelectricity • Good for creating charged objects. • Allows the study of basic electrical phenomena. • More qualitative than quantitative. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 7 More Positive * Human Hands (if very dry) * Leather * Rabbit Fur * Glass * Human Hair * Nylon * Wool * Fur * Lead * Silk * Aluminum * Paper * Cotton * Steel (neutral) * Wood * Amber * Hard Rubber * Nickel, Copper * Brass, Silver * Gold, Platinum * Polyester * Styrene (Styrofoam) * Saran Wrap * Polyurethane * Polyethylene (scotch tape) * Polypropylene Vinyl (PVC) * Silicon * Teflon More Negative The Triboelectric Series Lose electrons more easily Positive Positive Negative Negative MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 10 Triboelectricity Examples The rotation of helicopter blades in the atmosphere will generate a large electrostatic charge. A grounding hook is used to dissipate the charge on the helicopter before making contact with it. Static Tales: http://www.pprune.org/archive/index.php/t-309803.html Static Discharge Operation STATIC DISCHARGE HOOKUP MAN SAFETY SIDE TO RENDEZVOUS: POINT AIRCRAFT EMERGENCY LANDING AREA i... APPROACH MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 11 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 12 Electrostatic Discharge Example Walking on a carpet can build up a static charge. Static charges can damage sensitive electronic chips. Conductive wrist straps tied to ground dissipate these dangerous charges. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 15 Electrostatic Force Like charges repel MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 16 Electrostatic Force Unlike charges attract MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 17 Electrostatic Force Measurements • Electroscope - semi quantitative measurements • Torsion meter - quantitative measurements - fairly precise force measurements. • Electrometer and Charge Sensors MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 20 Electroscope Electroscope is negatively charged. Thin gold foil leaves MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 21 A Quantitative Electroscope A gold leaf electroscope measures potential difference between the leaf and the base (or earth). The leaf rises because it is repelled by the stem (support). The leaf and its support have the same type of charge. A typical school electroscope will show a deflection for a charge as small as 0.01 pC. The unit pC is a pico Coulomb, 1x10-12 Coulombs, equivalent to the charge on over 6 million electrons. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 22 Electroscope • Charging by direct contact • Charging by induction MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 25 Charge Distributions In the problems that you will be asked to solve in these first three chapters you will be asked to work with charge distributions and to calculate the resultant electric forces or fields. This is electrostatics - the charges are not moving when we try to describe them. However, the charges might move initially until they settle down in an equilibrium position. It is after they achieve this equilbirium position that we will apply the various equations of electrostatics. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 26 Uniform Charge Distributions These will be found in three forms: linear, surface and volume charge distributions. • Charge can be positive or negative. • Charges are fixed in location and don’t move. • Uniform means the charge per unit measure is constant. • The material containing these charges has only one property - It holds the charges in place and doesn’t respond to the Coulomb forces of the other charges. This is most similar to charges on a dielectric surface. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 27 Real Charge Distributions • In conductors there are free electrons that respond to external charges and fields. Except in high symmetry situations these real charge distributions are difficult to handle mathematically. • In dielectric materials (insulators) there are bound charges that while not free to move, are able to respond to electric fields in a limited way. • We will deal with conductors first and later with dielectrics. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 30 Relative Distance Vector Arbitrary coordinate system Electric force problems with point charges will be the most difficult problems that we will solve this semester. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 31 Coulomb Force Vectors Force on q2 due to q1. ( ) ( ) ˆ •








12 2 1 12 12 2 1 2 1 12 12 12 r = r - r r = r = r - r r - r r r = r MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 32 ˆ
1 2 12 122 12 q q F = k r r Coulomb’s Law 1 2 2 q q F = k R Simple scalar magnitude calculation Full blown vector description 9 2 2 0 0 -12 2 2 0 1 k = = 8.99x10 Nm /C 4πε ε ε = 8.85x10 C /Nm = Permittivity of free space MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 35 Opposite Charges - Attractive Force ˆ ˆ ˆ


2 12 2 -19 2 9 12 -10 2 -9 12 e F = -k i r (1.602x10 ) F = -(8.99x10 ) i (10 ) F = -23.1x10 i (N) Three quantities determine the direction of the force q1, q2, and 1̂2r MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 36 Maximize Force Charges q1 and q2 are separated by a distance D. The sum of the charges is held constant. What value of q2 maximizes the force between them? 1 2 1 22 kq q F = ; Q = q + q D ( ) 2 2 1 2 2 k Q - q q q = Q - q ; F = D ( )( )2 22 2 2 dF k d = Q - q q dq D dq MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 37 Maximize Force ( )( )2 22 2 2 dF k d = Q - q q = 0 dq D dq The maximum force is determined by setting the derivative of F with respect to q2 equal to zero. ( ) ( ) ( ) ( )          2 2 2 22 2 2 2 2 22 2 2 2 dF k d d = Q - q q + q Q - q = 0 dq D dq dq dF k = Q - q - q = 0 dq D Q Q - 2q = 0 q = 2 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 40 Problem Strategy The solution only describes the region x > 2.0m ( ) ˆ       


1 0 2 0 net 10 20 22 k q q k q q F = F + F = - i x x - 2.0 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 41 Electric Forces in 2-D MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 42 Electric Forces in 2-D ( ) ( ) 0 01 0 1 0 10 2 2 ˆ ˆcos(45 ) sin(45 ) 2 2 2 2 kq q kq q F i j= +
( )2 0 20 2 ˆ 2 kq q F j= + −
( ) 01 0 2 ˆcos(45 ) 2 2 x kq q F i=
( ) 2 001 0 2 2 ˆ ˆsin(45 ) 22 2 y k q qkq q F j j= + −
Electric Field Vectors E. AO Vip Field point P 1 ~ Source point 7 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 45 FCWARYA Some Electric Fields in Nature E, N/C In household wires 10 In radio waves 1071 In the atmosphere 10? In sunlight 10° Under a thundercloud 104 Ina lightning bolt 104 In an X-ray tube 10° At the electron ina hydrogen atom 6 x 104 At the surface of a uranium nucleus 2 x 107! MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 47 Electric Field Problems Dividing the problem into three regions avoids the need to develop a set of unit vectors that will work in all three regions. Looking for zero E-field No zero No zero Zero possible Electric Dipole Geometry y MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 50 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 51 Electric Dipole Field ( ) ˆ ˆ ˆ

22 2 4 3 4ax E = kq i for x > a x - a 4ax 4kqa E = kq i = i for x >> a x x The x-3 variation of the E- field is the characteristic of a dipole field - it is short ranged. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 52 Electric Dipole Vectors ˆ ˆ

4 3 3 4ax 2k(2qa) 2kp E = kq i = i = for x >> a x x x Electric Field Distribution (b) MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 55 MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 56 Electric Field Distribution MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 57 Electric Field Distribution MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 60 H20 Molecule The charge distribution of the water molecule gives rise to a permanent dipole moment. It’s the dipole moment that causes the water molecule to oscillate back and forth in the presence of a microwave field. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 61 Polarized Object in an External Electric Field The microwave field alternates direction at a frequency ~ 109 Hz MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 62 Polarized Object in an External Electric Field An electric field can polarize objects that don’t have a permanent dipole moment A non-uniform electric field can both polarize an object and attract it. MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 65 Hmwk Problem #73 Three charges on a line. q1 at x=0; q2 at x = 0.2 m; Q at x = 0.32m. Question: a.) Determine Q; b.) Find x so that E(x)=0ˆ
2F = 240N i 1 2 3 q = -3.0µC q = +4.0µC q = Q = -97.1 µC MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 66 Hmwk Problem #73 ( ) 2 1,2 Q,2 1 2 2 2 2 1,2 Q,2 F = F + F kq q kQq 240i = i + i r r −


ˆ ˆ ˆ ˆ ˆ ˆ       1 2 2 2 2 1,2 Q,2 2 Q,2 1 2 2 2 1,2 kq q kQq 240i = i - i r r -r kq q Q = 240 - kq r ˆˆ

Q,2 Q,2 Q,2 r r = = -i r MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 67 Hmwk Problem #73       2 Q,2 1 2 2 2 1,2 -r kq q Q = 240 - kq r ( ) ( )( ) ( )( )( ) ( )       2 2 - 0.12 8.99E + 09 -3E - 06 4E - 06 Q = 240 - 8.99E + 09 4E - 06 0.2 This is when the sign of the charge goes in. Q = -97.1 µC Electric Field (NiC} Electric Field - X-Axis + t 4 a t 388888888 t t ea t @ Resultant E Field ZHHREE8EE @qi EField + aq? E-Field mOE-Field t * -0 * * * * 00 MFMcGraw-PHY 2426 Distance Ch21b-Electric Fields-Revised 8/23/2012 70 Electric Field (NIC) Electric Field - X-Axis = oo on " “ ; ee x 7 od a —— 4aegee9 + + @ Resultant E Field é @qt EField aq? E-Field ° mQEField 0.300 oo MFMcGraw-PHY 2426 a ry : a a HABE ie a 4 a = + a Spnggcan =2 0888880 Distance Ch21b-Electric Fields-Revised 8/23/2012 71  +4 +4 4) MFMcGraw-PHY 2426 Ch21b-Electric Fields-Revised 8/23/2012 72