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Direct current (dc) generators Split ring (commutator) does the job of reversing polarity every half cycle Motional emf – conductor moving in a constant magnetic field B Blx FB qvB will move charges until compensated by the electric field of end accumulations qvB qE qV /l V Bvl dx Bl Blv dt Generators as Energy Converters I Blv / R Presistor I 2 R ( Blv )2 / R Generator does not produce electric energy out of nowhere – it is supplied by whatever entity that keeps the rod moving. All it does is to convert it to a different form, namely to electric energy (current) Who does the work? We! - By moving the bar: Papplied Fv IBlv ( Blv )2 / R Energy conserved After initial push, Rotating bar : velocity w ill relax v(r ) r Small element : decelerate d by the magnetic force : Bv dr d Total emf : l Bl 2 Br dr 2 0 2 m dv ( Bl ) IBl v dt R v v0 exp( t / ) mR /( Bl ) 2 Motion does not necessarily mean changing magnetic flux! Significance of the minus sign – Lenz’s Law Induced current has such direction that its own flux opposes the change of the external magnetic flux Magnetic field of the induced current wants to decrease the total flux Magnetic field of the induced current wants to increase the total flux Correspondingly, magnetic forces oppose the motion – consistently with conservation of energy! Lenz’s Law – the direction of any magnetic induction effect as to oppose the cause of the effect Lenz’s Law – a direct consequence of the energy conservation principle Finding the direction of the induced current Induced Electric Fields No matter wha t , the total force on a charge is F q (E v B ) To have current in the loop, F 0 We did explain currents in moving conductors (" motional emf" ) with FB qv B BUT! Faraday' s experiment s show that currents are induced when v 0 but B B(t ) What is it that drives charges then? Electric field E induced by changing B ! emf is nothing but the work done to move a unit charge around the loop once, which is the line integral around the loop E ds Electric field around a solenoid with alternating current Current : I(t) Imax cos(t) Magnetic field inside the solenoid : B(t) 0 nI(t) (outside B 0) Flux through the surface bounded by the path B (t) B(t) R 2 Electric field circulation around the path E ds E 2r : : dB 0 nImax R 2 sin( t) dt Outside : E(r,t) 0 nImax R 2 sin( t) 2r nI r Inside ( R r) : E(r,t) 0 max sin( t) 2 B What Maxwell equation w orks is E t Using Stokes' theorem : B E ds S ( E) n dA S t n dA B B n dA !!! t S t The electric field E generated by changing B is very different from the electrosta tic E : now it is time - dependent E(t ) and nonconserv ative Do we need a real circuit to have this field? - NO! We cannot change magnitude of the velocity of a charged particle in a static magnetic field B BUT We can do it in a time-varying magnetic field B(t) – the resulting electric field E(t) will do the job And that’s indeed how particles are accelerated in betatrons! Space Weather Causes Currents in Electric Power Grids Electric currents in Earth's atmosphere can induce currents the planet's crust and oceans. During space weather disturbances, currents associated with the aurora as large as a million-amperes flow through the ionosphere at high latitudes. These currents are not steady but are fluctuating constantly in space and time - produce fluctuating magnetic fields that are felt at the Earth's surface - cause currents called GICs (ground induced currents) to flow in large-scale conductors, both natural (like the rocks in Earth's crust or salty ocean water) and man-made structures (like pipelines, transoceanic cables, and power lines). Some rocks carry current better than others. Igneous rocks do not conduct electricity very well so the currents tend to take the path of least resistance and flow through man-made conductors that are present on the surface (like pipelines or cables). Regions of North America have significant amounts of igneous rock and thus are particularly susceptible to the effects of GICs on man-made systems. Currents flowing in the ocean contribute to GICs by entering along coastlines. GICs can enter the complex grid of transmission lines that deliver power through their grounding points. The GICs are DC flows. Under extreme space weather conditions, these GICs can cause serious problems for the operation of the power distribution networks by disrupting the operation of transformers that step voltages up and down throughout the network.