Synopsis : 8. ELECTROMAGNETISM

Size: px

Start display at page:

Download "Synopsis : 8. ELECTROMAGNETISM"

Berenice Park
5 years ago
Views:

1 Synopss : 8. ELECTROMAGNETISM MAGNETIC EFFECTS OF CURRENT: 1. Electomagnetsm s the banch of physcs whch deals wth elaton between electcty and magnetsm.. A statc chage poduces only electc feld but movng chage poduces both electc feld and magnetc feld n space. 3. Movng chage cuent s the souce of magnetc feld. 4. Oested n 180 AD obseved that magnetc feld s poduced by a cuent cayng conducto. 5. Ampee establshed elatonshp between the cuent n the conducto and stength of the magnetc feld aound the conducto. 6. Oested s expement : A magnetc compass needle placed n the vcnty of a conducto cayng conducto algned pependcula to the conducto. 7. The decton of deflecton of noth pole of magnetc needle s gven by Ampee s swmmng ule. 8. Ampee s swmmng ule : Imagne that a man s swmmng along the conducto n the decton of the cuent facng a magnetc needle the noth pole of the needle wll deflect towads hs left hand. S N 9. The magnetc lnes of foce aound a cuent cayng conducto ae concentc ccles wth the cente lyng on the conducto. 10. The decton of magnetc feld aound the cuent cayng conducto s gven by a) Maxwell s cok scew ule b) Rght hand thumb ule Maxwell s cok scew ule : Imagne a ght hand scew s advancng n the decton of cuent n a conducto. Then the decton of otaton of the scew gves the decton of magnetc lnes of nducton. Rght hand thumb ule : Imagne that a cuent cayng conducto s held n the ght hand palm such that the decton of cuent s ndcated by the thumb. Then the othe fnges ndcate the decton of magnetc lnes of nducton. 11. Ampee s law : Ampee s law states that the lne ntegal of B B. dl along a closed dl path ound the cuent cayng conducto s equal to μ o whee s the cuent though the suface bounded by the closed path and μ o pemeablty of fee space. B.dl B π = μo μo B = π = μo 1. Bot-Savat s law : The magnetc nducton at a pont nea a cuent cayng conducto s dectly popotonal to the length of the conducto, the stength of the cuent and sne of the angle made by the lne jonng the pont wth the conducto and nvesely popotonal to the squae of the dstance of the pont μo.dl. sn θ μ o db =. ; db =. d l x 3 1

2 Electomagnetsm The decton of magnetc nducton s gven by the vecto ( d l x ). Ths law s vald only fo small cuent segments. 13. Ampee's law and Bot-Savat law ae equvalent but Ampee's law s moe useful n some symmetcal condtons. A 14. The magnetc nducton at a pont P due to a conducto of fnte length s α B = (snα + snβ) β P 15. The magnetc feld nducton due to the cuent cayng conducto of B nfnte length s gven by B μ 0 μ = o B = 0 π B μ0 Magnetc feld at one end of nfnte long conducto s B = 16. The magnetc feld nducton due to the long cuent cayng cylndcal conducto s B = π (R + ) Whee R s the adus of the conducto and s the dstance of the pont fom the suface of the conducto at whch the value of B s gven. Howeve f >>R, then B μ = 0 π 17. The magnetc feld nducton at a pont along the axs of a ccula col s μ0 πn B = whee n = numbe of tuns, = cuent n the col, = adus and x = the 3 / ( + x ) dstance of the pont fom the cente of the col. na B = 3 / ( + x ) na If x >>, then B = 3 x M.e., B = whee M = magnetc moment of the cuent loop. 3 x 18. (a) The magnetc feld nducton at the cente of a ccula col of n tuns s gven by elaton μ n B = 0 α μ0 (b) Magnetc feld nducton at the cente of an ac s B = α 19. Fo a solenod of fnte length at any pont on the axs B μ 0 = N R α β [sn α + snβ] ; L N s numbe of tuns pe unt length. 0. A solenod conssts of closely wounded helcal col. Insde the solenod the feld s almost unfom. μ n The magnetc nducton at the cente of the solenod s B = 0 whee l s the axal length and n s l total numbe of tuns n length l of the solenod. The equaton holds good only when the adus of the tuns s vey small when compaed wth the length. 1. When cuent s passed though a helcal spng, t contacts due to mutual attacton between consecutve tuns. Foce on a movng chage n a magnetc feld :

3 3 Electomagnetsm. An electc chage movng n a unfom magnetc feld expeences a foce (F). F = q(v x B) o F = qvb sn θ 3. The decton of foce s obtaned by ght hand gp ule. When the chage entes nto a unfom magnetc feld pependcula to ts decton, then F = qvb. If t entes along the decton of the feld, F = The foce can only change the decton n whch the chage s movng but not ts speed. Hence no wok s done by t. 5. When a chaged patcle moves n a unfom magnetc feld at ght angles to the decton of the feld. ) the tajectoy of moton changes and ) the speed and enegy of a patcle eman the same. 6. When a chaged patcle moves n an electc feld, wok s done and hence ts knetc enegy nceases. 7. If we assume that the eath s magnetc feld s due to a long ccula loop of cuent n the nteo of the eath, then the plane of the loop wll be east-west and the cuent passes n clockwse decton when seen fom eath s noth pole. 8. An electon s movng vetcally downwads at a cetan place. The decton of foce on t due to the hozontal component of the eath s magnetc feld s towads west. 9. The foce actng on a chaged patcle when t entes a unfom magnetc feld of nducton B, wth velocty v at ght angles to the feld wll povde the necessay centpetal foce and make the chaged patcle move along a ccula path of adus. F = mv qvb = ; mv v qb = o = qb m π πm sn ce T =, we have T = ω qb Thus tme peod s ndependent of the patcle-speed. Hence the faste patcles move n bgge ccles and slowe patcles move n smalle ccles such that the peod of evoluton T s the same. qb 30. The fequency ( ν ) = and s called cycloton fequency. πm 31. If a chaged patcle entes a unfom magnetc feld along the lne of the feld, t goes undevated. If t entes at an angle of nclnaton othe than 90 o to the feld, ts path s helcal. 3. When both the electc and magnetc felds ae pesent, the total foce on q s F = qe + qv x B. Ths foce s known as Loentz foce. 33. The fequency of a chaged patcle n a unfom magnetc feld s known as cycloton fequency as the patcles n a ccula acceleato, called cycloton, move wth ths fequency. 34. Cycloton s a devce used to acceleate chaged patcles to hgh speed fo nuclea eacton. It was nvented by Lawence. The foce on a cuent cayng conducto n a magnetc feld : 35. When a conducto of length l cayng a cuent s placed at an angle θ to the decton of the magnetc feld of flux densty o nducton B, the foce on the conducto o we s gven by F = ( l x B) o F = lb sn θ Its decton can be detemned by usng Flemng s left hand ule, whose statement s as follows: Stetch the foe fnge, mddle fnge and thumb of the left hand mutually pependcula to each othe. If the foe fnge epesents the decton of magnetc feld, the mddle fnge that of cuent, then the thumb wll epesent the decton of foce on the conducto. Foce & toque on cuent loop o col n a magnetc feld : 36. The total magnetc foce on any closed cuent loop n a unfom magnetc feld s zeo.

4 4 Electomagnetsm 37. Toque o couple on a cuent cayng ectangula conducto o loop n a unfom magnetc feld s gven by τ = AB sn θ whee A s the aea of the ectangula loop, B s the magnetc nducton and θ s the angle between the nomal to the plane of the ectangula loop and the feld. If thee ae n tuns, then the toque actng on the col suspended s gven by τ = nab sn θ o τ = MB sn θ whee M s the magnetc dpole moment equal to na and θ s the angle between the magnetc nducton and the nomal to the plane of the col.e., the decton of the magnetc moment. When the plane of the col makes an angle θ wth the feld, then the couple actng on the col s τ = nabcos θ o τ = MBCos θ. 38. If 1 and ae the stengths of cuents passng though two nfntely long, staght and paallel wes sepaated by a dstance, the magnetc feld nducton B, due to the flow of cuent n the 1 fst conducto at a dstance on the second conducto s B1 =. π The foce exeted by ths nducton on a length l on the second conducto s F = B1l 1 The foce pe unt length s F =. π If the cuent s n the same decton, thee wll be attacton and f the cuent s passng n opposte decton, thee wll be epulson. 39. An ampee s that steady cuent when flowng n each of two long staght paallel wes sepaated by a dstance of one mete apat n vacuum causes each we exet to each othe a foce of x10-7 N pe each mete length of we. Movng col galvanomete : 40. A movng col galvanomete conssts of a poweful hose shoe magnet wth concave poles to poduce a unfom adal magnetc feld. On a cylndcal soft on coe, a col s wound and the col s suspended wth a phosphobonze fbe. The plane of the col always les n the decton of the magnetc feld because the magnetc feld s adal. The whole appaatus s kept nsde a bass case povded wth a glass wndow. Cθ = ampee NAB Hee C s the couple pe unt twst on the suspenson fbe, s the cuent passng though the galvanomete col and θ s the angle of deflecton by the needle. C/BAN s a constant (k) s called as galvanomete constant. Deflecton s measued moe accuately usng Lamp and Scale aangement. The ay eflected onto the scale by the mo s deflected by 'x'. The dstance between the mo attached to the suspenson fbe of the galvanomete and the scale s D, then Tan θ θ when θ s vey small x x C x Then θ = ; θ = ; =. D D BAN D 41. The cuent senstvty of a galvanomete s the deflecton n mm poduced on a scale kept at a dstance of one mete by a constant cuent of one mcoampee. 4. The ecpocal of the cuent senstvty s called fgue of met and s expessed n μ A/mm. 43. A cuent upto 10 9 A can be measued usng movng col galvanomete. 44. Table Galvanomete : It has a ectangula col of nsulated coppe suppoted on two beangs. The poles of the magnet ae concave. It has a lght alumnum ponte whch moves on a scale. The whole aangement s kept n an ebonte case wth a glass wndow. 45. Compason of MCG wth TG :

5 Movng Col Galvanomete MCG s a movng col type galvanomete and the col otates n a magnetc feld when cuent s passed though the col. The plane of the col need not be algned n magnetc nducton. The cuent flowng though the col s dectly popotonal to the deflecton. It s accuate and can be used to measue the cuents of ode 10 9 A wth pope desgn. The galvanomete constant does not depend on eath s magnetc feld. Stay magnetc felds have no effect on t and can be used fo the measuement of the cuents even n mnes. Electomagnetsm Tangent Galvanomete TG s a movng magnet type galvanomete. The magnetc needle otates when cuent s passed though the col. The plane of the col must be n magnetc medan. The cuent flowng n the col s popotonal to the tangent of deflecton. Tan values ae not so accuate and can be used to measue the cuents of the ode 10 6 A. The galvanomete educton facto depends on eath s magnetc feld whch s dffeent at dffeent places. Extenal felds have effect on t and theefoe TG cannot be used n mnes. Tangent Galvanomete : 46. a) It s potable and mnmum measuable cuent s of the ode of 10 6 A. b) woks on the pncple of Tangent law B= B H Tanθ μ Hee B = Magnetc nducton due to passage of cuent n the col = 0 B c) cuent measued by Tangent galvanomete s H = Tanθ = KTanθ μ0n = Radus of col n = numbe of tuns of col d 1 d) Readng s moe accuate when θ = 45 snce elatve eo α and t s mnmum fo sn θ 45 dθ e) Senstveness s maxmum when θ = 0 snce senstveness αcosθ, whch s maxmum fo θ d = 0. f) Dung expement, plane of the col should be along the magnetc medan [to fulfll the equement of tangent law] 47. Shunt : a) A low esstance connected n paallel to galvanomete to potect t fom lage cuent s known as shunt. b) = g + s ( S) c) g = ( G) d) s = e) g s S = = 1 n 5

6 Electomagnetsm GS f) effectve esstance of ccut = g) If the ange of galvanomete s nceased to n tmes, 1/n th of man cuent passes though galvanomete. Hence senstveness decease by n tmes. 48. Ammete : a) It s a devce used to measue cuent n electcal ccuts. b) Galvanomete can be conveted n to Ammete by connectng low esstance paallel to t. c) To ncease the ange by n tmes o to decease the Senstveness by n tmes, shunt to be connected acoss Galvanomete. g( G) G S = = g ( n 1) Hee n = g new ange old dvdsons / A = = old ange new dvsons / A GS d) Resstance of Ammete = e) Resstance of deal Ammete s zeo and ts conductvty s nfnty f) Ammete must be always connected n sees to the conducto. g) Among low ange and hgh ange Ammete, low ange Ammete has moe esstance. h) As shunt value deceases senstvty deceases, accuacy nceases. 49. Voltmete : a) Voltmete s a devce used to measue P.D. acoss the conducto n electc ccuts. b) Galvanomete s conveted nto voltmete by connectng hgh esstance n sees to t. c) Voltmete s always connected n paallel to the conducto [P.D. acoss whch s to be measued] V d) Resstance of voltmete = G +R = g e) Hee V s ange of voltmete (e) esstance of deal voltmete s nfnty and conductvty s zeo. f) Among low ange and hgh ange voltmetes, hgh ange voltmete has moe esstance. g) P.D. acoss the ends of voltmete s, V = g +(G+R) V h) Resstance to be connected n sees to galvanomete to convet nto voltmete s R = G. g ) To ncease the ange by n tmes, new angev n = old angev1 g ( G + R) = g ( G) R = 1+ G Hence esstance to be connected n sees to galvanomete s R = G(n-1). j) As sees esste value nceases senstvty deceases, accuacy nceases 6

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig.

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig. TEST-03 TPC: MAGNETSM AND MAGNETC EFFECT F CURRENT Q. Fnd the magnetc feld ntensty due to a thn we cayng cuent n the Fg. - R 0 ( + tan) R () 0 ( ) R 0 ( + ) R 0 ( + tan ) R Q. Electons emtted wth neglgble