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MIT 8 02X - Electricity and Magnetism

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Feb 18 2005 web.mit.edu/8.02x/wwwElectricity and Magnetism• Review for 8.02x Quiz #1– Electric Charge and Coulomb’s Force– Electric Field and Field Lines– Superposition principle– E.S. Induction– Electric Dipole– Electric Flux and Gauss’ Law– Electric Potential Energy and Electric PotentialFeb 18 2005 web.mit.edu/8.02x/wwwQuiz• Material as covered in class (this review)• Evening Review in 54-100, 7PM, today• Question(s) on demos (or similar setup)– all demos are fair game• No question on LVPS/HVPS – but exp questions in future quizzes• All you need is a pen• You can bring a letter-size formula sheet– submitted together with quiz• Quiz in room 26-100 TUESDAY 10AMFeb 18 2005 web.mit.edu/8.02x/wwwElectric Charge and Electrostatic Force• New Property of Matter: Electric Charge–comes in two flavors: ‘+’ and ‘-’• Connected to Electrostatic Force–attractive (for ‘+-’) or repulsive (‘- -’, `++’)• Charge is conserved• Charge is quantized •Neutral: Equal amount of + and - Feb 18 2005 web.mit.edu/8.02x/wwwAtomsElementary ParticlesMoleculesEarthSolar SystemFarthest GalaxyHumanStrength10-201015110-1510-1010-510510101020Atomic NucleiWeak ForceStrong ForceElectric ForceGravity110-3610-7100[m]Feb 18 2005 web.mit.edu/8.02x/wwwCoulomb’s Law•Inverse square law (F ~ 1/r2)• Gives magnitude and direction of Force• Attractive or repulsive depending on sign of Q1Q2Feb 18 2005 web.mit.edu/8.02x/wwwCoulomb’s LawQ1Q2F12r21r21Feb 18 2005 web.mit.edu/8.02x/wwwCoulomb’s LawQ1Q2F12r21r21Feb 18 2005 web.mit.edu/8.02x/wwwCoulomb’s LawQ1Q2F12r21r21F12 = - F 21Feb 18 2005 web.mit.edu/8.02x/wwwSuperposition principle• Note:– Total force is given by vector sum– Watch out for the charge signs– Use symmetry when possibleQ1Q2F12Q3F13F1,totalFeb 18 2005 web.mit.edu/8.02x/wwwSuperposition principle• If we have many, many charges– Approximate with continous distribution• Replace sum with integral!Feb 18 2005 web.mit.edu/8.02x/wwwElectric Field• New concept – Electric Field E• Charge Q gives rise to a Vector Field• E is defined by strength and direction of force on small test charge qFeb 18 2005 web.mit.edu/8.02x/www• Electric Field also exists is test charge q is not present• The charge Q gives rise to a property of space itself – the Electric Field• For more than one charge -> Superposition principleThe Electric FieldFeb 18 2005 web.mit.edu/8.02x/www• For a single chargeElectric FieldFeb 18 2005 web.mit.edu/8.02x/www• For a single charge• Visualize using Field Lines Electric Field+QFeb 18 2005 web.mit.edu/8.02x/wwwField Lines• Rules for field lines–Direction: Tangential to E at each point–Density: Shows magnitude of E– Field Lines never cross– From positive to negative charge• i.e. show direction of force on a positive charge– Far away: Everything looks like point charge Feb 18 2005 web.mit.edu/8.02x/www• Field Lines for two unlike charges:Example of Field LinesHaliday: Fundamentals of PhysicsFeb 18 2005 web.mit.edu/8.02x/wwwTorque ! = p x Ep = Q l DipolemomentElectric DipoleFeb 18 2005 web.mit.edu/8.02x/wwwElectrostatic Induction+++++++++++• Approach neutral object with charged objectFeb 18 2005 web.mit.edu/8.02x/wwwElectrostatic Induction• Approach neutral object with charged object• Induce charge separation (dipole)• Force between charged and globally neutral object– if field is non-uniform+++++++++++++++++------Feb 18 2005 web.mit.edu/8.02x/www•Electric Flux: "E = E A• No ‘substance’ flowing• Flux tells us how much field ‘passes’ through surface AElectric FluxFeb 18 2005 web.mit.edu/8.02x/wwwElectric Flux• For ‘complicated’ surfaces and/or non-constant E:– Use integral• Often, ‘closed’ surfacesFeb 18 2005 web.mit.edu/8.02x/www• Example of closed surface: Box (no charge inside)•Flux in (left) = -Flux out (right): "E = 0Electric FluxdAdAEFeb 18 2005 web.mit.edu/8.02x/wwwGauss’ Law• How are flux and charge connected?•Charge Qencl as source of flux through closed surfaceFeb 18 2005 web.mit.edu/8.02x/wwwGauss’ Law•True for ANY closed surface around Qencl • Relates charges (cause) and field (effect)• Coulombs Law follows from Gauss’ LawFeb 18 2005 web.mit.edu/8.02x/wwwGauss’ Law• Most uses of Gauss’ Law rely on simple symmetries– Spherical symmetry– Cylinder symmetry– (infinite) plane• and remember, E = 0 inside conductorsFeb 18 2005 web.mit.edu/8.02x/wwwGauss’ Law• Different uses for Gauss’ Law–Field E -> Qencl (e.g. conductor)–Qencl -> Field E (e.g. charged sphere)• Proper choice of surface – use symmetriesFeb 18 2005 web.mit.edu/8.02x/wwwHollow conducting Sphere++++++++++++++++++++++++++++++++++Feb 18 2005 web.mit.edu/8.02x/wwwGauss’ LawdAQ•Charge Sphere radius r0, charge Q, r > r0r0rQencl = QFeb 18 2005 web.mit.edu/8.02x/wwwWork and Potential EnergyxxabdlF(l)Work: #Conservative Force: Potential Energy Feb 18 2005 web.mit.edu/8.02x/wwwElectric Potential Energy• Electric Force is conservative– all radial forces are conservative (e.g. Gravity)• We can define Electric Potential EnergyFFeb 18 2005 web.mit.edu/8.02x/wwwElectric Potential• Electric Potential Energy proportional to q• Define V = U/q •Electric Potential V: – Unit is Volt [V] = [J/C]Feb 18 2005 web.mit.edu/8.02x/wwwElectric Potential• Note: because V = U/q -> U = V q– for a given V: U can be positive or negative, depending on sign of q• V :Work per unit charge to bring q from a to bFeb 18 2005 web.mit.edu/8.02x/www+++++++++++-----------ba+qxaxbx=0xx=dExample: Large parallel platesFeb 18 2005 web.mit.edu/8.02x/wwwExample: Large parallel plates+++++++++++-----------ba+qxaxbxV(x)xx=0xU(x,q)0q>0q<0x=dFeb 18 2005 web.mit.edu/8.02x/wwwConductors• Conductor: Charges can move around (unlike insulator)• E = 0 inside – otherwise charges would move• No charges inside – Gauss• E perpendicular to surface (close to surface)– otherwise charges on surface would


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