Physics 2102Physics 2102Lecture 02: THU 21 JANLecture 02: THU 21 JANElectric Fields IElectric Fields IPhysics 2102Jonathan DowlingCharles-Augustin de Coulomb (1736-1806)What Are We Going to Learn?What Are We Going to Learn?A Road MapA Road Map• Electric charge- Electric force on other electric charges- Electric field, and electric potential• Moving electric charges : current• Electronic circuit components: batteries, resistors,capacitors• Electric currents - Magnetic field- Magnetic force on moving charges• Time-varying magnetic field & Electric Field• More circuit components: inductors.• Electromagnetic waves - light waves• Geometrical Optics (light rays).• Physical optics (light waves)2q!12F1q+21F12rCoulombCoulomb’’s Laws Law2122112||||||rqqkF =2212001085.8with 41mNCk!"==#$#2291099.8CmN!k =For Charges in aVacuumOften, we write k as:Charles-Augustin de Coulomb (1736-1806)ElectricForce FieldSir Michael Faraday’s Electric Lines of Force Faraday (1791–1867)E-Field is E-Force Divided by E-ChargeE-Field is E-Force Divided by E-ChargeDefinition ofElectric Field: ! E =! F q |! F 12|=k | q1| | q2|r122+q1–q2 ! F 12P1P2 |! E 12|=k | q2|r122–q2 ! E 12P1P2Units: F!=![N]! =![Newton]; E!=![N/C]! =![Newton/Coulomb]E-ForceonChargeE-FieldatPointElectric FieldsElectric Fields• Electric field E at some point in space isdefined as the force experienced by animaginary point charge of +1 C, dividedby 1 C.• Note that E is a VECTOR.• Since E is the force per unit charge, itis measured in units of N/C.• We measure the electric field usingvery small “test charges”, and dividingthe measured force by the magnitude ofthe charge.2||||RqkE =–qRE+1CElectric Field of a Point ChargeSuperposition of F and ESuperposition of F and E• Question: How do we figure outthe force or field due toseveral point charges?• Answer: consider one charge ata time, calculate the field (avector!) produced by eachcharge, and then add all thevectors! (“superposition”)• Useful to look out forSYMMETRY to simplifycalculations!• If you never learned to addvectors in 2101 you’ll be inserious trouble in 2102!See online reviewhttp://phys.lsu.edu/~jdowling/PHYS21024SP10/Vectors.pdfExample• 4 charges are placed at the corners ofa square as shown.• What is the direction of the electricfield at the center of the square?(a) Field is ZERO!(b) Along +y(c) Along +x-q-2q+2q+qyxTotal electric field !E !!F+q+q ! +1.0C+q is the test chargeElectric Field Lines• Field lines: useful way tovisualize electric field E• Field lines start at a positivecharge, end at negativecharge• E at any point in space istangential to field line• Field lines are closer where Eis strongerExample: a negative pointcharge — note sphericalsymmetryDirection of Electric Field LinesE-Field VectorsPoint Away fromPositive Charge —Field Source!E-Field VectorsPoint TowardsNegative Charge— Field Sink!Electric Field of a DipoleElectric Field of a Dipole• Electric dipole: two point charges+q and –q separated by adistance d• Common arrangement in Nature:molecules, antennae, …• Note axial or cylindricalsymmetry• Define “dipole moment” vector p:from –q to +q, with magnitude qdCancer, Cisplatin and electric dipoles:http://chemcases.com/cisplat/cisplat01.htmElectric Field On Axis of DipoleElectric Field On Axis of Dipole!++= EEE :ionSuperposit22!"#$%&'=+axkqE22!"#$%&+'='axkqE!!!!"#$$$$%&'()*+,+-'()*+,-=222121axaxkqE22242!!"#$$%&'=axxakqPax-q+qax-q+qElectric Field Electric Field OnOn Axis of Dipole Axis of Dipole2222224242!!"#$$%&'=!!"#$$%&'=axkpxaxxakqEWhat if x>> a? (i.e. very far away)p = qa“dipole moment”a VECTOR- +3422xkpxkpxE =!E!=!p/r3 is actually true for ANY point far from adipole (not just on
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