Chapter 31Faradays LawElectricity generator, or from B to E.1. Battery Chemical emf2. Motional emf3. Faradays Law of Indction!. Len"s Law a#ot the emf directionA dry-cell batteryChemical reactions in the #attery cells trans$ort charge carriers %electrons& from one terminal to the other to create the needed electric $otential %emf& to dri'e the crrent throgh the otside load, a light #l# here. Motional emf, the conceptq = F v Br rrq = F v Br rr= = =B EF qvB F qE(hen e)ili#rim(ith(e can gro$ charges #y mo'ing them in a magnetic field motional emf.* motional emf is the emf indced in a condctor mo'ing throgh a magnetic field+he electrons in the condctor e,$erience a force, that is directed along Charges are accumulated at the ends of the conductor to create an electric feld inside the conductor to stop further charge transportation. q = F v Br rrMotional emf, the calculation-tart from the e)ili#rim condition.ne has.r the emf, $otential difference/*s long as the #ar is 0e$t mo'ing with a 'elocity ', the motional emf is maintained to #e vB. = = =B EF qvB F qE= E vB= = = emf V E vB l lMotional emf, put in use to power a resistorBar mo'ed #y rappFI+wo isses need attention/1. +he mo'ing #ar carrying crrent I, inside the magnetic field, e,$eriences a force from the field is FB=IB2. +he magnetic fl, in the enclosed area %#ar, rails and resistor& is B=xB, and it is changing with time as E)i'alent circit diagram Condition/* #ar mo'ing on two rails. +he #ar and the rails ha'e negligi#le resistance. * resistor of 1 is connected to the end of the two rails. 1eslt/+he emf 2 vB, so the crrent I 2 vB /R( )= = = =bd d dxx B B vBdt dt dtemf l l lEample, what is the terminal velocity!* #ar of mass m sides on two 'ertical rails. * resistor is connected to the end of the rails. (hen the #ar is released at t = t0, %a& calclate the 'elocity of the #ar at time t, %#& what is the terminal 'elocity3 *ssming that the rails and the magnetic field is long4large enogh. Im= emf vBl=rG mg F .nce the #ar starts to mo'e, accelerated #y the gra'itational force, there is/*nd there is crrent as well/= I vB R l /*nd there is magnetic force on the #ar, $ointing o$$osite to the gra'itational force/( )= = r2Bv BI BRFllEample, what is the terminal velocity!Im=rG mg F Constrct the e)ation of 'elocity v/-ol'e this e)ation +his is the answer to %a&. For %#&, the terminal 'elocity is when ( )( ) + = = =r rr22G Bv Bmg mv Bdvmg mdtRRF F a ll( ) = 2dv dt mR,v gB l( ) = = = Q 1 5 5tv g e , v tg tFaraday"s #aw of inductionIn the sliding #ar 6e,$eriment7, we $ro'ed that/=bddtemf(e also 0now that the magnetic fl, is defined ascos = =r r or B Bd BA B AIn the sliding #ar e,$eriment, we changed A #y mo'ing the #ar. More $ractically $eo$le change B or the angle to achie'e a changing fl,. Changing B Changing Faraday"s #aw of inductionIn any case, the indced emf follows the Faradays Law of indction /6the emf id!"ed i a "i#"!it i$ di#e"t%& p#'p'#ti'a% t' the time #ate 'f "hage 'f the mageti" f%!x th#'!gh the "i#"!it7bddt#en$"s #aw the direction of the induced emf#en$"s law/ ()he id!"ed "!##et i a %''p i$ i the di#e"ti' that "#eate$ a mageti" fie%d that 'pp'$e$ the "hage i mageti" f%!x th#'!gh the a#ea e"%'$ed b& the %''p* i.e. the indced crrent tends to 0ee$ the original magnetic fl, throgh the circit from changing.Bd+dt= Len"s LawEample% EMF produced by a chan&in& ma&netic field* loo$ of wire is connected to a sensiti'e ammeter8etermine the crrent in the loo$ when the magnet is #eingMo'ed into the loo$Mo'ed ot of the loo$9eld still inside the loo$Eample% a transformer* $rimary coil is connected to a switch and a #attery+he wire is wra$$ed arond an iron ring* secondary coil is also wra$$ed arond the iron ring+here is no #attery $resent in the secondary coil+he secondary coil is not directly connected to the $rimary coil Eample, #en$"s #awApplications of Faraday"s #aw ' (F) * :FI %grond falt indicator& $rotects sers of electrical a$$liances against electric shoc0(hen the crrents in the wires are in o$$osite directions, the fl, is "ero(hen the retrn crrent in wire 2 changes, the fl, is no longer "ero+he reslting indced emf can #e sed to trigger a circit #rea0er*otatin& #oop*ssme a loo$ with , trns, all of the same area rotating in a magnetic field+he fl, throgh the loo$ at any time t is B 2 BA cos 2 BA cos t-osin= =Bdemf , ,BA- -tdt+he emf is a sin wa'e/ *C.(eneratorsElectric generators ta0e in energy #y wor0 and transfer it ot #y electrical transmission+he *C generator consists of a loo$ of wire rotated #y some e,ternal means in a magnetic field+C (enerators+he 8C %direct crrent& generator has essentially the same com$onents as the *C generator+he main difference is that the contacts to the rotating loo$ are made sing a s$lit ring called a "'mm!tat'#MotorsMotors are de'ices into which energy is transferred #y electrical transmission while energy is transferred ot #y wor0* motor is a generator o$erating in re'erse* crrent is s$$lied to the coil #y a #attery and the tor)e acting on the crrent;carrying coil cases it to rotateMotors, cont,