NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s long s the flu linked with the cicuit chnges. The phenomenon is clled electomgnetic induction MAGNTC FLUX s.ds.ds d GAUSS S LAW FOR MAGNTSM.dS 0 FARADAY S LAW Fdy pefomed thee epeiment : peiment 1: He pulled loop of wie to the ight though mgnetic field s soon figue (). A cuent flowed in the loop. peiment : He moed the mgnet to the left, holding the loop still s soon figue (). Agin, cuent flowed in the loop. peiment 3: With oth the loop nd the mgnet t est s soon figue (c), he chnge the stength of the field (he used n electomgnet, nd ied the cuent in the coil). Once gin cuent flowed in the loop. () () chnging mgnetic field The fist epeiment, of couse, is n emple of motionl emf, coneniently epessed y the flu ule: d Fdy hd n ingenious inspition: A chnging mgnetic field induces n electic field. t is this induced electic field tht ccounts fo the emf in peiment. ndeed, if (s Fdy found empiiclly) the emf is gin equl to the te of chnge of the flu, d.dl (c)
then is elted to the chnge in y the eqution.dl.d t This is Fdy s lw, in integl fom. mple 1 : A coil is plced in constnt mgnetic field.the mgnetic field is pllel to the plne of the coil s shown in figue. Find the emf induced in the coil. mple : = 0 (lwys) since e is pependicul to mgnetic field. emf = 0 Figue shows coil plced in decesing mgnetic field pplied pependicul to the plne of coil.the mgnetic field is decesing t te of 10T/s. Find out cuent in mgnitude nd diection LNZ S LAW =.A emf = A. d = 10 = 0 i = 0/ 5 = 4 mp. Fom lenz s lw diection of cuent will e nticlockwise. The induced cuent will flow in such diection tht the flu it poduces tends to cncel the chnge. l d c d c i=0 d c () () (c) Refe figue () A loop cd entes unifom mgnetic field t constnt speed. Using Fdy s eqution, d d(s) d( / ) d e l l Fo the diection of cuent, we cn use Lenz s lw. As the loop entes the field mgnetic field pssing though the loop inceses, hence, cuent in the loop is nticlockwise. ( N). Fom the theoy of motionl emf, e l nd using ight hnd ule, cuent in the cicuit is nticlockwise. Thus, d we see tht e nd e l gie the sme esult. n the simil mnne we cn show tht cuent in the lop in figue () is zeo nd in figue (c) it is clockwise. NDUCD MF N A ROD e l sin
mple 3 : A od PQ of length L moes with unifom elocity pllel to long stight wie cying cuent. The end P emins t fied pependicul distnce fom the wie. Clculte the e.m.f. induced coss the od. The od moes in the mgnetic field poduced y the cuent cying wie s esult of which n e.m.f. is induced coss the od. Let us conside smll element of length d of the od t distnce nd + d fom the wie. The e.m.f. induced coss the element, d d (1) P +d The mgnetic field t distnce fom wie cying cuent is gien y 0 () Using () in (1), we get 0 d d (3) nduced emf coss the entie length of the od PQ is gien y Q 0 d d L P 0 d L d 0 0 loge log e ( L) log e 0 L loge 0 L L Q NDUCTOR Aledy we he studied out cpcito tht stoes enegy in the fom of electic field. Like cpcito, inducto is lso quite commonly used element in electic cicuits, which stoes mgnetic enegy. nductnce of n inducto depends on its geomety nd medium in which it lies. As we know tht when cuent flows though conducto mgnetic field is set-up ound it, nd hence it is ssocited with mgnetic flu. f mgnetic flu ssocited with coil is nd cuent in it is, then its inductnce is gien y the epession L. 'L' is clled self-inductnce of the coil. S.. unit of inductnce is heny. NDUCD MF N A ROTATNG COL SLF NDUCTANC e NA sint e0 sin t d di e L CALCULATON OF SLF-NDUCTANCS () A long stight solenoid : L 0n [ l ] Fo ey long solenoid, l > > nd eqution educes to
NA 0n l 0 L () An open-i tnsmission line : l l d 0 L ln (c) A coil cle : l 0 L ln MUTUAL NDUCATNC e S d dip M CALCULATON OF MUTUAL NDUCTANCS () Two solenoids : M mna n = nume of tuns pe unit length of the pimy solenoid m = nume of tuns pe unit length of the secondy solenoid () Two pllel coil cicul loops: N N M 0 1 3 ( ) mple 4 : Wht is the self inductnce of system of co-il cles cying cuent in opposite diections s shown. Thei dii e nd espectiely. The etween the spce of the cles is = o / The Ampee s lw tells tht outside the cles is zeo, s the net cuent though the mpein loop would e zeo. R D Tking n element of length nd thickness d, d though it is 1 d d d ln 0 0 0 0 L ln SLF-NDUCTANCS N SRS AND PARALLL () Seies connection : L L1 L M L1L M () Pllel connection : L L1 L M RLATON TWN SLF AND MUTUAL NDUCTANC : COFFCNT OF COUPLNG M k LL 1 Thus fo n idel coupling, k 1 o M L1L And fo non-idel coupling, k 1 o M L1L 0 k 1 mple 5 : Figue shows two concentic copln coils with dii nd ( << ). A cuent i = t flows in the smlle loop. Neglecting self inductnce of lge loop
() Find the mutul inductnce of the two coils ( Find the emf induced in the lge coil (c) f the esistnce of the lge loop is R find the cuent in it s function of time () To find mutul inductnce, it does not mtte in which coil we conside cuent nd in which flu is clculted (Recipocity theoem) Let cuent i e flowing in the lge 0 coil. Mgnetic field t the cente = i () (iii) flu though the smlle coil = 0 M i 0 di 0 emf induced in lge coil M in smlle coil 0 0 cuent in the lge coil R NDUCD LCTRC FLD in This electic field hs following impotnt popeties : () t is non consetie in ntue. The line integl of ound closed pth is not zeo. When chge q goes once ound the loop, the totl wok done on it y the electic field is equl to q times the emf. Hence.d d e Note, tht the eqution is lid only if the pth ound which we integte is sttiony. () (c) (d) ecuse of symmety, the electic field t seel points on the loop e shown in figue. eing non-consetie field, the concept of potentil hs no mening fo such field. This field is diffeent fom the electosttic field poduced y sttiony chges (which is consetie in ntue). (e) The eltion F q is still lid fo this field.
(f) This field cn y with time. A chnging mgnetic field cts s souce of electic field tht cnnot e poduced with ny sttic chge distiution. mple 6 : Find the mgnitude of induced field " n " t point (>R) whee unifom ut time ying mgnetic field d = eists in egion of dius R. Fo the cicul pth of dius '' n.d = n () s n.d we get, n. = R d R d = = d [No mgnetic field fo > R] R