11From Last Time…Static electric chargesInteractions betweencharges2Properties of electric charge• Two types of charges Positive and negative• Interactions between charges Like charges repel Unlike charges attract Interaction decreases with increasing distance3Vector Nature of Electric Forcea)The force is repulsive if charges are of like signb)The force is attractive if charges are of opposite signThe force is a conservative forceElectrical forces obey Newton’s Third Law:F21 = -F124Quick QuizTwo charges are arranged as shown.What is the direction of the force on thethe positively charged ‘test’ particle?++ABCDE5Magnitude of force:Coulomb’s Law• Electrical force between two stationary charged particles• The SI unit of charge is the coulomb (C ), µC = 10-6 C• 1 C corresponds to 6.24 x 1018 electrons or protons• ke = Coulomb constant ≈ 9 x 109 N.m2/C2 = 1/(4πεo)εo = permittivity of free space = 8.854 x 10-12 C2 / N.m26Quick QuizAbout what is the force between two particles 1 mapart, each with charge 100 micro-Coulomb?ke=9x109 N-m2/C2A. 100 NB. 1 NC. 1000 ND. 0.1 NE. 0.00127+--Equal but opposite chargesare connected by a rigid insulating rod.They are placed near a negative charge as shown.What is the net force on the two connected charges?A) LeftB) RightC) UpD) DownE) Zero221rqkqF =Quick Quiz8The electric dipole• Can all be approximatedby electric dipole.• Two opposite chargesmagnitude qseparated by distance sDipole momentVectorPoints from - charge to + chargeHas magnitude qs ! r p 9Induced dipoles (charge redistribution)Bring negative charge close.Electrons on spheremove away from rod.charged rubber rod10Induced dipole in insulators• A process similar toinduction can take place ininsulators• The charges within themolecules of the materialare rearranged11Quick QuizTwo uniformly-charge spheres are firmly fastened to, andelectrically insulated from, frictionless pucks on an air table.The charge on sphere 2 is three times the charge on sphere 1.Which choice below correctly shows the magnitude anddirection of the forces? ABCDE12The idea of electric fields• EM wave made up ofoscillating electric and magnetic fields.• But what is an electric field?• Electric field is a way to describe the force ona charged particle due to other chargesaround it.• Force = charge × electric field• The direction of the force is the direction ofthe electric field.313Electric field of a point charge++Force on this charge……due to this charge+++ ! Force = Charge( ) " Electric field( ) ! r F = kQ1Q2r2ˆ r Q1Q214Question• Which vector best represents theelectric field at the red dot?ABCDE-ABC-DE15Relationship Between F and E• Fe = qE This is valid for a test charge smallenough that it does not disturb thesource charge distribution• If q is positive, F and E are in the same direction+r = 1x10-10 mQp=1.6x10-19 CEE = (9×109)(1.6×10-19)/(10-10)2 N = 2.9×1011 N/C(to the right)16Electric Field Direction• a) q is positive, F isdirected away from q• b) The direction of E isalso away from thepositive source charge• c) q is negative, F isdirected toward q• d) E is also toward thenegative source charge17Superposition with Electric Fields• At any point P, the total electric field due to a group ofsource charges equals the vector sum of electric fields ofall the chargesFind the electric field due to q1, E1Find the electric field due to q2, E2E = E1 + E2Remember, the fields add as vectors18Quick QuizWhich is the direction of the electric field at dot?A. LeftB. RightC. UpD. DownE. Zero+-xyAway from positive charge (right)Net E field is to right.419Quick QuizWhat is the direction of the electric field at point A?A. UpB. DownC. LeftD. RightE. Zero1) Zero+-xy20Electric field: summary• Electric field ->will be a force on a charged particle.• This force ( and electric field) can arisefrom electric charges (via Coulomb’slaw)• But once electric field is known, don’tneed to know the charges that produceit.21Pictorial representation of E: Electric Field Lines22Electric field lines• Local electric field tangent to field line• Density of lines proportional to electricfield strength• Fields lines can only start on + charge• Can only end on - charge.• Electric field lines can never cross23Electric field of a dipole+-24Electric field of two +
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