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Electricity and Magnetism

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Electricity and Magnetism Electricity and Magnetism • Review – 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 Potential – Conductors, Isolators and Semi-Conductors Feb 27 2002 Today • Fast summary of all material so far – show logical sequence – help discover topics to refresh for Friday Feb 27 2002 Electric Charge and Electrostatic Force • New Property of Matter: Electric Charge –comes in two kinds: ‘+’and ‘-’ •Connected toElectrostatic Force –attractive(for ‘+-’) or repulsive (‘--’, `++’) •Charge is conserved •Charge isquantized Feb 27 2002 Strength 10-20 -7 Elementary Particles Weak Force 10 Atomic Nuclei 10-15 Strong Force 100 Atoms 10-10 Molecules Electric Force 1 10-5 Human 1 Earth 105 -36 1010 Gravity 10 Solar System 1015 1020 Feb 27 2002 Farthest Galaxy Coulomb’s Law • Inverse square law (F ~ 1/r2) • Gives magnitude and direction of Force • Attractive or repulsive depending on sign of Q1Q2 Feb 27 2002 Coulomb’s Law F12 r21 Q1 Q r21 2 Feb 27 2002 Coulomb’s Law r21 Q1 F12 = - F 21 F12 r 21 Q2 Feb 27 2002 Superposition principle Q3 F13 Q1 F1,total F12 Q2 •Note: – Total force is given by vector sum – Watch out for the charge signs – Use symmetry when possible Feb 27 2002 Superposition principle • If we have many, many charges – Approximate with continous distribution • Replace sum with integral! Feb 27 2002 Electric 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 q Feb 27 2002 The Electric Field • 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 principle Feb 27 2002 Electric Field • For a single charge +Q • Visualize using Field Lines Feb 27 2002 Field Lines • Rules for field lines – Direction: In direction of 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 27 2002 Electric Dipole Torque τ = p x E p = Q l Dipole moment Feb 27 2002 Electrostatic Induction • Approach neutral object with charged object + ++ --++ • Induce charges (dipole) + + - + + + - ++ • Force between charged and + + - + + + globally neutral object Feb 27 2002 Electric Flux • Electric Flux: ΦE = E A • Same mathematical form as water flow •No ‘substance’flowing • Flux tells us how much field ‘passes’ through surface A Feb 27 2002 Electric Flux • For ‘complicated’ surfaces and non-constant E: –Use integral • Often, ‘closed’ surfaces Feb 27 2002 Electric Flux • Example of closed surface: Box (no charge inside) dA dA E • Flux in (left) = -Flux out (right): ΦE = 0 Feb 27 2002 Gauss’ Law • How are flux and charge connected? •Charge Qencl as source of flux through closed surface Feb 27 2002 Gauss’ Law • True for ANY closed surface around Qencl • Relates charges (cause) and field (effect) Feb 27 2002 Gauss’ Law • Different uses for Gauss’ Law – Field E -> Qencl (e.g. conductor) – Qencl -> Field E (e.g. charged sphere) • Proper choice of surface – use symmetries Feb 27 2002 Hollow conducting Sphere + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Feb 27 2002 Gauss’ Law • Charge Sphere radius r0, charge Q, r > r0 dA Q r0 r Qencl = Q Feb 27 2002 Gauss’ Law • Most uses of Gauss’ Law rely on simple symmetries – Spherical symmetry – Cylinder symmetry –(infinite) plane • and remember, E = 0 in conductors Feb 27 2002 Work and Potential Energy F(l) b dl x α x Work: a Conservative Force: Potential Energy Feb 27 2002 Electric Potential Energy • Electric Force is conservative – all radial forces are conservative (e.g. Gravity) • We can define Electric Potential Energy F Feb 27 2002 Example: Two charges Q q r •If q,Q same sign: – U > 0; we have to do work ‘pushing’ charges together •If q,Q unlike sign: – U < 0; Electric force does work ‘pulling’ charges together Feb 27 2002 Electric Potential • Electric Potential Energy proportional to q •Define V = U/q • Electric Potential V: – Units are Volt [V] = [J/C] Feb 27 2002 Electric 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 b •Ex.:Single Charge Feb 27 2002 Electric Potential for many charges • Superposition principle.... V(x) = Σ1/(4πε0) Qi/ri • Sum of scalars, not vectors! • Integral for continous distributions Feb 27 2002 Example: Three charges Q2 Q3 Q1 r2 r3 r1 V(x) = Σ1/(4πε0) Qi/ri x Feb 27 2002 Example: Capacitor plates + - + - + - + - + - + a b - + +q - + - + - + - x x a b x x=0Feb 27 2002 x=d Example: Capacitor plates V(x) 0 + - x + - + - + - + - a b + - U(x,q) q<0 + +q - + - + - x + - x x a b x x=0Feb 27 2002 x=d q>0 Applications + - + - + - • Energy for single particle + (e.g. electron) small Velocity v - + - +q •Often measured in + - ‘Electron Volt’[eV] + - + - • Energy aquired by + - particle of charge 10-19 C + - going through ∆V=1V d Feb 27 2002 Conductors •E = 0 inside – otherwise charges would move • No charges inside –Gauss • E perpendicular to surface – otherwise charges on surface would move • Potential is constant on conductor Feb 27 2002.
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