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Introduction n n n n n n n n n n n n n Vending machine Electricity generator and motor Electric guitar Train brake Wireless battery charger Airport metal detector Transformer Radio and TV CD player and tape cassette Sunglass Sail on sunlight Photos More Brief review of E & M • Gauss’s law Qin FE = Ú E • dA = e0 What is Gauss’s law for magnetic field? † • Ampere’s law dQ Ú B • ds = m0 I = m0 dt • Lorentz force law † † F = qE + qV ¥ B † Faraday’s law FB = Ú B • dA dFB e = -N dt The emf induced in a circuit is directly proportional to the time rate of change of magnetic†flux through the circuit. FB = † † † † Ú B • dA = B • A = BA cosq d e = - (BAcosq ) dt • B =B(t) • A = A(t) • q = q(t) • Any combinations d - cos wt = w sin wt q = wt dt e = BAw sin wt If there are N turns, what is the emf ? † † Example 31.1 A coil consists of 200 turns of wire having a total resistance of 2.0 W. Each turn is a square of side 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.8s, what is the magnitude of induced emf in the coil, and what is induced current? dF B | e |= N dt F B = AB cosq = AB cos 0 = AB dF B d(AB) dB = =A dt dt dt † N = 200, A = (0.18m)2 , | e |= 4.1V |e | I= = 2.0A R † dB 0.50T - 0T = dt 0.80s Motional emf qE = qvB E = vB e = DV = El = Blv † † Does†a current flow? Is there a voltage? Lenz’s law The polarity of induced emf is such that it tends to produce a current that creates a magnetic flux (Lorentz force) to oppose the change in magnetic flux through the area enclosed by the current loop (the motion of a conductor) Example 31.2 Blv R R Blv B 2l 2 v FB = IlB = (lB) = R R † e = Blv † e I= = Application of Lenz’s law Find the direction of the current induced in the ring. Eddy Current: Application of Lenz’s law † Induced electric field and electrostatic field • Induced electrical field produced by changing magnetic flux dF B e = - dt e = Ú E • ds dF B e = Ú E • ds = - dt ≠ 0 † Nonconservative Induce electric field in vacuum • Electrostatic field produced by stationary charges Ú E • ds = 0 Conservative † DV = 0 Example 31.8 B = 0, r > R B = m0 nI, r < R 2 † for r>R F B = BpR F B = Bpr 2 for r<R B = m0 nI = m0 nI max cos wt † E • ds = E(2 pr) E • ds = - dF B E(2 pr) = - dF B Ú Ú dt dt † 2 m nI w R † E = 0 max sin wt for r>R 2r † maxw † m0 nI E= r sin wt for r<R 2 Maxwell’s Equations Q ÚÚ E • dA = e 0 ÚÚ B • dA = 0 dF B Ú E • ds = - dt dF E Ú B • ds = m0 I + e0m0 dt F = qE + qV ¥ B †