January 14, 09Physics 2102Physics 2102Lecture: 03 FRI 16 JANLecture: 03 FRI 16 JANElectric Fields IElectric Fields ICharles-Augustin de Coulomb (1736-1806)Physics 2102Jonathan DowlingVersion: 1/14/09What 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 è 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: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 inspace is defined as the forceexperienced by an imag i nary pointcharge of +1 C, divided by 1 C.• Note that E is a VECTOR.• Since E is the force per unit charge,it is measured in units of N/C.• We m easure the electric field usingvery small “test charges”, anddividing the measured force by themagnitude of the charge.2||||RqkE =–qRE+1CElectric Field of a Point ChargeSuperposition of F and ESuperposition of F and E• Question: How do wefigure out the force orfield due to severalpoint charges?• Answer: consider onecharge at a time,calculate the field (avector!) produced byeach charge, and thenadd all the vectors!(“superposition”)• Useful to look out forSYMMETRY to simplifycalculations!Example• 4 charges are placed at thecorners of a square as shown.• What is the direction of theelectric field at the center ofthe square?(a) Field is ZERO!(b) Along +y(c) Along +x-q-2q+2q+qyxTotal electric fieldElectric Field Lines• Field lines: useful way tovisualize electric field E• Field lines start at apositive charge, end atnegative charge• E at any point in spaceis tangential to field line• Field lines are closerwhere E is 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 pointcharges +q and –qseparated by a distance d• Common arrangement inNature: 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 axis)3rpE!!!Force on a Charge in Electric FieldForce on a Charge in Electric FieldDefinition ofElectric Field: ! ! E =! F qForce onCharge Due toElectric Field: ! ! F = q! EForce on a Charge in Electric FieldForce on a Charge in Electric FieldEEPositive ChargeForce in SameDirection as E-FieldNegative ChargeForce in OppositeDirection as E-Field+ + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – –Electric Dipole in a Uniform FieldElectric Dipole in a Uniform Field• Net force on dipole = 0;center of mass stays whereit is.• Net TORQUE τ : INTO page.Dipole rotates to line up indirection of E.• | τ | = 2(qE)(d/2)(sin θ)= (qd)(E)sinθ= |p| E sinθ= |p x E|• The dipole tends to “align”itself with the field lines.• What happens if the field isNOT UNIFORM??Distance BetweenCharges =
View Full Document