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Chapter 34. Electromagnetic Induction Electromagnetic induction is the scientific principle that underlies many modern technologies, from the generation of electricity to communications and data storage. Chapter Goal: To understand and apply electromagnetic induction. Chapter 34. Electromagnetic Induction Topics: • Induced Currents • Motional emf • Magnetic Flux • Lenz’s Law • Faraday’s Law • Induced Fields • Induced Currents: Three Applications • Inductors • LC Circuits • LR Circuits Stop to think 34.1 page 1044 Stop to think 34.2 page 1045 Stop to think 34.3 page 1048 Stop to think 34.4 page 1054 Stop to think 34.5 page 1058 Stop to think 34.6 page 1067 Stop to think 34.7 page 1073 Faraday’s Discovery Faraday found that there is a current in a coil of wire if and only if the magnetic field passing through the coil is changing. This is an informal statement of Faraday’s law. Magnetic data storage encodes information in a pattern of alternating magnetic fields. When these fields move past a small pick-up coil, the changing magnetic field creates an induced current in the coil. This current is amplified into a sequence of voltage pulses that represent the 0s and 1s of digital data. Motional emf FB qvB E F q vB m o tio n al em f l l vlB V Vtop Vbottom 0 E y dy 0 ( vB ) dy vBl Potential difference along a rotating bar V V tip V pivot l 0 E r dr l 0 ( rB ) dr 1 2 l B 2 Induced Current in a Circuit I R vlB R F p u ll Fm a g IlB ( vlB R 2 ) lB vl B R 2 P 1046 Magnetic flux can be defined in terms of an area vector The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle θ from the field, B. As a dot-product, the equation becomes AB cosθ Example 34.5 Magnetic flux from the current in a long straight wire (P1051) From the Chapter 33. we know the magnetic field at distance x from a long straight wire : B 0I 2 x The infinitesimal flux through a little area is d m B dA BdA m dm dm dt 0 Ib 2 ca c 0I 2 x dx x b dx 0 Ib 2 c a ln c 0 Ib 0 Ib c a d ln d / dt 2 c 2 0 Ib a V 2 c (c a ) ln (1 a / c / dt ) The Induced current for six different situation Tactics: Using Lenz’s Law coil N dm dt ABN d (cos t ) dt A B N sin( t ) V em w ave 1 00 Inductors • Capacitors: as devices that produce a uniform electric field. • Capacitance: C = Q/ΔV • Capacitor stores potential energy UC =1/2 C(ΔV)2 • Inductors: A coil of wire in the form of a solenoid is a device that produces a uniform magnetic field. An idea inductor is one for which the wire forming a coil has no electric resistance . • The magnetic filed inside a solenoid having N turn and length l B 0 NI • We define the inductance L as: L m I • The inductance of the solenoid: l • L (solenoid) = N 0 N A 2 per coil I l From Faraday’s Law N dm N d ( BA) dt L so len o id dt 0 N l 2 A N d ( 0 N I / lA ) dt 0 N A / l 2 dI dt Inductance of a solenoid The inductance of a solenoid having N turns, length l and cross-section area A is Here we also used the magnetic field B (solenoid) : B 0 NI l (equation 33.16, P 1017) Energy density: The potential difference across an inductor The potential difference across an inductor with an inductance of L and carrying a current I measured along the direction of the current is IR L dI dt o r IR L Q 0 C dI dt Q C C Q L C Q dI 0 dt L C dI 2 L dt Q ( t ) Q 0 cos( t ) P 1070 d Q dt 2 1 LC LR Circuits L dI IR 0 dt I I0e dI I t /( L / R ) I0e R dt L t / =L / R A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? A. There is no current around the loop. B. There is a clockwise current around the loop. C. There is a counterclockwise current around the loop.