MAGNETIC EFFECT OF CURRENT AND E.M.I.

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3 MGETC EFFECT OF CUET D E.M.. ETH S MGETC FELD The eath behaves as a huge ba magnet with its magnetic field on its suface and upto a height of about 3 4 km. Geogaphical oth Magnetic South The magnetic field of the eath is attibuted to one o moe of the following causes:- S (i) nothe point of view attibutes the eath s magnetism is the pesence of ion and nickel in the coe of the eath. t is assumed that the otation of the eath about its own axis causes the magnetisation of the ion and nickel and the eath behaves as a ba magnet. (ii) of. Blackett, studied that the otation of the eath about its own axis causes eath s magnetism. Fo example, the pesence of ions in the uppe atmosphee constitutes a cuent due to the otation of the eath about its own axis. Long ago, it has been known that eath has a magnetic field, which is vey simila to the field poduced by a huge magnet which is supposed to be at its cente. ts noth pole lies towads the geogaphic south and south pole towads the geogaphic noth. The axis of the eath s magnetic field does not coincide with the geogaphic axis, the angle between them being about 5. The positions of the magnetic poles ae not well defined on the globe, they ae spead ove an aea. The magnetic pole in the nothen hemisphee is located on a peninsula in nothen Canada. The opposite magnetic pole in the southen hemisphee lies on the ntactic continent, south of ustalia. The eath s magnetic field is supposed to aise fom electic cuents in the molten ion ich oute coe suounding the solid inne coe of the eath. Figue shows some field lines in the eath s magnetic field. The field lines usually dip towads o come out of the eath s suface at some angle. This angle is called the magnetic inclination o the magnetic dip at that place. t the magnetic poles, the angle of dip is 9º. The line on the eath s suface passing though the places having angle of dip is called the magnetic equato, it passes though Thumba in south ndia, whee the space eseach cente is located. Magnetic oth S Geogaphical South Geogaphical Equato ELEMETS OF ETH S MGETC FELD The following thee quantities ae called elements of eath s magnetic field. (a) ngle of declination : (b) ngle of dip (o nclination) (c) Hoizontal component of eath s magnetic field (a) ngle of Declination : The vetical plane passing though the axis of a feely suspended magnet is called magnetic meidian. The diection of eath s magnetic field lies in the magnetic meidian and may not be hoizontal. The vetical plane passing though the tue geogaphical noth and south (o geogaphical axis of eath) is called geogaphical meidian. The angle between the magnetic meidian and the geogaphic meidian at a place is called angle of declination at that place. The knowledge of declination at a place helps in finding the tue geogaphical diections at that place. n ou county, the angle of declination is zeo in ondichey. Geogaphic meidian O G ngle of declination Magnetic meidian JSO STGE-_GE #

4 (b) ngle of Dip (o ngle of nclination) : The angle between the axis of a feely suspended magnetic needle (which is fee to otate in the vetical plane) and the hoizontal plane at a place is called the angle of dip (o inclination) at that place. Hoizontal plane ngle of dip H M Magnetic needle (c) Hoizontal Component of Eath s Magnetic Field : Let be the total intensity of eath s magnetic field. t a place the total intensity of eath s magnetic field can be esolved into two components i.e. hoizontal component H and vetical component V. H cos...(i) V sin...(ii) Whee is the angle of dip at a place. on dividing equation (ii) by (i) tan H V...(iii) Magnetic axis (i) ngle of dip at the poles : The magnetic lines of foce at the poles of eath ae vetical due to which the magnetic needle becomes vetical. Thus the angle of dip at the magnetic poles of the eath is 9. fom equation (i) and (ii) Dip Cicle ngle of dip at the equato : The lines of foce aound the magnetic equato of the eath ae pefectly hoizontal. So, the magnetic needle will become hoizontal thee. Thus, the angle of dip at the magnetic equato of the eath will be as shown in figue. The line on the eath s suface passing though the places whee the angle of dip is is called magnetic equato. 3 V H...(iv) BOT-SVT S LW ( B DUE TO WE) t is an expeimental law. Let cuent i flows in a wie (may be staight o cuved). Due to wie the magnetic field at is : db id db db sin Combining these equations, we get id sin db d length of the i...(i)...(ii) d...(iii) Dip Cicle 3º 3º 6º 9º 6º º º 6º 6º 3º 3º id sin db 4 Vecto epesentation db id 3 4 Hee position vecto of the test point with espect 9º to (w..t.) d angle between d and. Using this fundamental fomula we can deive the expession of B due to a long wie. JSO STGE-_GE #

5 (a) B due to a staight wie : Due to a staight wie Q caying a cuent, the B at ULE FO FDG DECTO OF MGETC FELD The diection of the magnetic field at a point due to a staight wie can be found by a slight vaiation in the ight hand thumb ule. f we stetch the thumb of the ight hand along the cuent and cul ou finges to pass though the point, the diection of the finges at gives the diection of the magnetic field thee. by the fomula : oint is given Q B (sin + sin 4 ) (i.e., diection of B is inwad pependicula to the plane of page) Special case : (i) f the wie is infinitely long then the magnetic field at (as shown in the figue) is given by (using 9º and the fomula of B due to staight wie) LLUSTTOS. hoizontal ovehead powe line caies a cuent of 9 in east to west diection. What is the magnitude and diection of the magnetic field due to the cuent.5 m below the line? Sol. 9º,.5 m B T.5 E 7 B S W B B 7 B 8 T..5 5 T Magnetic field is towads south. The diection of B at vaious is as shown in the figue. The magnetic lines of foce will be concentic cicles aound the wie (as shown ealie) (ii) f the wie is infinitely long but is as shown in the figue. The diection of B at vaious points is as shown in the figue and magnetic field atpoint B 4 upto 9º. Find esultant magnetic field at C in the figue shown. S C i 3 a Sol: t is clea that B at C due all the wies is diected. lso B at C due Q and S is same. lso due to Q and S is same B es (B Q + B S ) Q a JSO STGE-_GE # 3

6 B Q B sp i a 4 4 i 3a B es (sin 6º + sin 6º), (sin 3º + sin 3º) 3 i i 4i a a 3 3a 3. Figue shows a squae loop made fom a unifom wie. Find the magnetic field at the cente of the squae if a battey is connected between the points and C. D Sol. The cuent will be equally divided at. The fields at the cente due to the cuents in the wies B and DC will be equal in magnitude and opposite in diection. The esultant of these two fields will be zeo. Similaly, the esultant of the fields due to the wies D and BC will be zeo. Hence, the net field at the cente will be zeo. 4. n the figue shown thee ae two paallel long wies (placed in the plane of pape) ae caying cuents and conside points, C, D on the line pependicula to both the wies and also in the plane of the pape. The distances ae mentioned. Find (i) B at, C, D C B (ii) position of point on line C D whee B is O. at C : B is and B also B es B + B a a at D : B is and B is magnitude. B es 6 a 3 a and both ae equal in (ii) t is clea fom the above solution that B at point D. (b) B due to cicula loop : (i) t cente : Due to each d element of the loop, B at point c is inwads (in this case). B esultant at point c is. (inwads) B, c o. of the tuns in the loop., length of the loop can be faction,, etc. o intege Diection of B : The diection of the magnetic field at the cente of a cicula wie can be obtained using the ight-hand thumb ule. f the finges ae culed along the cuent, the stetched thumb will point towads the magnetic field (see figue ). C D a a/ a a Sol. (i) Let us call B due to () and () as B and B espectively. Then at : B is and B is B a and B B es B B 4 3 a a nothe way to find the diection is to look into the loop along its axis. f the cuent is in anticlockwise diection, the magnetic field is towads the viewe. f the cuent is in clockwise diection, the field is away fom the viewe. Semicicula and Quate of a cicle : B 8 4 ote : Magnetic field due to an ac is B i JSO STGE-_GE # 4

7 5. wie as shown in figue caies a cuent ampee. The cicula pat has a adius. The magnetic field at the cente C will be : Sol. Magnetic field at the cente due to C and BC is zeo. the magnetic field at the cente will only due to the C 3 th pat of the cicula loop. 4 Magnetic field at C staight wie caying a cuent of q is bent ito a semicicula ac of adius. cm as shown in Figue (a). What is the diection and magnitude of B at the cente of the ac? Would you answe change if the wie wee bent into a semicicula ac of the same adius but in the opposite way as shown in Fig. 4.9(b)? Sol. (i) Magnetic field at he cente of the ac is B 4 Hee,.cm. m, 4 7 Tm 7 4 B.9 4 T. 4. ccoding to ight hand ule the diection of the field is nomally into the plane of pape. (ii) The magnetic field will be of same magnitude, B.9 4 T. The diection of the field is nomally out of the plane of pape. 7. long wie is bent as shown in figue. What will be the magnitude and diection of the field at the cente O of the cicula potion, if a cuent is passed though the wie? ssume that the vaious potions of the wie do not touch at point. B C O Sol. The system consists of a staight conducto and a cicula loop Field due to staight conducto at point O is B, up the plane of pape Field due to cicula loop at point O is B, up th plane of pape Total field at O is B B +B, up the plane of pape. 9. Figue shows a cuent loop having two cicula segments and joined by two adial lines Find the magnetic field at the cente O. S a O Q b Sol. Since the point O lines S and Q so the magnetic field at O due to these staight potions is zeo. The magnetic field at O due to the cicula segment Q is B 4 a Hee, l length of ac Q a B 4 diected nomally upwad a Similaly, the magnetic field at O due to the cicula segment S is B 4, diected nomally downwad. b The esultant field at O is B B B 4 a b (b a) o B 4ab JSO STGE-_GE # 5

8 MGETC FOCE O MOVG CHGE Sol. Magnetic field at a distance of cm fom cuent caying conducto XY is When a chage q moves with velocity v in a magnetic field B, then the magnetic foce expeienced by moving chage is given by following fomula : F q( v B ), (ut value of q with sign), v and B emain in the same plane B B T v : nstantaneous velocity B : Magnetic field at that point. OTE : electon cm B (i) F v and also F B (Hee is symbol fo pependicula) x 5 Y (ii) F v powe due to magnetic foce on a chaged paticle is zeo. (use the fomula of powe F. v fo its poof). (iii) Since F B so wok done by magnetic foce is zeo in evey pat of the motion. The magnetic foce cannot incease o decease the speed (o kinetic enegy) of a chaged paticle. t can only change the diection of velocity. (iv) On a stationay chaged paticle, magnetic foce is zeo. (v) f v B, then also magnetic foce on chaged paticle is zeo. t moves along a staight line if only magnetic field is acting. (Hee is symbol fo paallel). n infinitely long staight conducto XY is caying a cuent of 5. n electon is moving with a speed of 5 m/s paallel to the conducto in ai fom point to B, as shown in figue. The pependicula distance between the electon and the conducto XY is cm. Calculate the magnitude of the foce expeienced by the electon. Wite the diection of the foce. B 5 6 T Foce expeienced by the electon is F evb ( 9º) ccoding to Fleming s left hand ule diection of foce will be upwads.. chaged paticle of mass 5 mg and chage q +C has velocity v î 3 ĵ 4kˆ. Find out the magnetic foce on the chaged paticle and its acceleation at this instant due to magnetic field B 3 ĵ kˆ. v and B ae in m/s and Wb/m espectively. Sol. F qv B 6 ( î 3ĵ 4kˆ ) ( 3 ĵ kˆ ) 6 [ 6 î + 4 ĵ + 6 kˆ ] F By ewton s Law a 6 m ( 3î ĵ 3kˆ ) m/s ( 6î 4 ĵ 6kˆ) electon cm x 5 B Y MGETC FLUX f we conside a plane pependicula to a unifom magnetic field, then the poduct of the magnitude of the field and the aea of the plane is called the magnetic flux () linked with that plane. The magnetic flux linked with this plane is given by B JSO STGE-_GE # 6

9 f the magnetic field B, instead of being pependicula to the plane, makes an angle with the pependicula to the plane as shown in figue, then the magnetic flux linked with the plane will be equal to the poduct of the component of the magnetic field pependicula to the plane and the aea of the plane. Thus, (B cos) B cos...(i) same diection as B. t is negative if the outwad nomal is opposite to B. S.. unit of B and : The S.. unit of magnetic flux is webe (Wb). Since B /, the magnetic field is also expessed in webe/mete, (Wb-m ). That is why the magnetic field induction B is also called the magnetic flux density. Definition of magnetic flux density (B) : B, if mete, then B n a magnetic field the numbe of lines of foce (flux) passing though pe mete pependicula to the field is equal to the magnetic flux density. Case : f º, then fom equation (i) B cos B (outgoing flux). The plane of a coil of aea m and having 5 tuns is pependicula to a magnetic field of 3 5 webe/ m. Find the magnetic flux linked with it. Sol. B cos but 5, B 3 5 wb/m, m, o B webe Case : f 9º, then fom equation (i) B cos9 B, Case : f 8º, then fom equation (i) B cos8 B (incoming flux) B FDY S LWS OF ELECTOMGETC DUCTO (i) When magnetic flux passing though a loop changes with time o magnetic lines of foce ae cut by a conducting wie then an e.m.f. is poduced in the loop o in that wie. This e.m.f. is called induced e.m.f. f the cicuit is closed then the cuent will be called induced cuent. (ii) n case of loop, the magnitude of induced e.m.f. is equal to the ate of change of flux w..t. time. n case of a wie it is equal to the ate at which magnetic lines of foce ae cut by a wie. d E dt ( ) sign indicates that the e.m.f. will be induced in such a way that it will oppose the change of flux. S.. unit of magnetic flux is webe, so S.. unit of induced e.m.f. is Wb Second Volt is positive if the outwad nomal to the plane is in the JSO STGE-_GE # 7

10 LEZ S LW ccoding to this law, e.m.f. will be induced in such a way that it will oppose the cause which has poduced it. Figue shows a magnet appoaching a ing with its noth pole towads the ing. const. emf 5. Find the diection of induced cuent in the coil shown in figue. Magnetic field is pependicula to the plane of coil and it is inceasing with time. Sol. nwad flux is inceasing with time. To opposite it outwad magnetic field should be induced. Hence cuent will flow anticlockwise. SELF DUCTCE We know that magnetic field lines come out of the noth pole and magnetic field intensity inceases as we move towads the magnet. f we conside the appoach of oth pole to be the cause of flux change, the lenz s law suggests that the side of the coil towads the magnet will behave as oth pole and will epel the magnet. We know that a cuent caying coil will behave like oth pole if cuent in it flows anticlockwise, as seen in figue. f we conside the appoach of magnet as the cause of the flux change, Lenz s law suggest that a foce opposite to the motion of magnet will act on the magnet, whateve be the mechanism. Lenz s law tells that if the coil is set fee, it will move away fom magnet, because in doing so it will oppose the appoach of magnet f the magnet is given some initial velocity towads the coil and is eleased, it will slow down. t can be explained as the following. The cuent induced in the coil will poduce heat. Fom the enegy consevation, if heat is poduced, thee must be an equal decease of enegy in some othe fom, hee it is the kinetic enegy of the moving magnet. Thus the magnet must slow down. So we can justify that the lenz s law is consevation of enegy pinciple. 3. coil is placed in a constant magnetic field.the magnetic field is paallel to the plane of the coil as shown in figue. Find the emf induced in the coil. Sol. (always) since aea is pependicula to magnetic field. emf 4. Find the emf induced in the coil shown in figue. The magnetic field is pependicula to the plane of the coil and is constant. ea Sol. B (always) B B When cuent flows though a coil o cicuit, magnetic field is poduced and hence a magnetic flux gets associated with this coil o cicuit. This magnetic flux is diectly popotional to the cuent flowing in the cicuit (f othe factos emain constant). f cuent though the coil is changed, the magnetic field is poduced and hence the magnetic flux associated with it changes and as a esult of which, an e.m.f. is induced in the coil o cicuit, ccoding to Lenz s law the diection of induced e.m.f. is such as that it always opposes change due to which it is poduced. s shown in figue, if cuent inceases in cicuit, induced e.m.f. is set up in such a way that it will decease the cuent i.e., induced cuent poduced due to induced e.m.f. flows opposite to the main cuent. Similaly, if main cuent deceases in the cicuit, induced e.m.f. will incease it. ow, the induced cuent due to induced e.m.f. will flow in the diection of main cuent. n this way the phenomenon, in which, on changing the cuent in a coil o cicuit an induced e.m.f. is set up in that coil o cicuit, is called self induction. This induced e.m.f. is called back e.m.f. (a) Coefficient of Self nductance : nduction o Self When cuent flows in a cicuit, associated magnetic flux is popotional to the cuent flowing i.e., o L...(i) Hee, L is a constant of popotionality, called the Coefficient of self-induction o self-inductance. Self-inductance of a coil depends on its aea, numbe of tuns and the medium inside it (mateial of coe). f, then L. Hence, self-inductance of a coil is equal to the magnetic flux associated with the coil when JSO STGE-_GE # 8

11 unit cuent flows though it. n equation (i), on changing the cuent, will also change and an induced e.m.f. E is poduced in the cicuit i.e., d( ) d(l) d E L dt dt dt d o L E if /s dt Hence, the coefficient of self induction in a cicuit is numeically equal to the induced e.m.f. poduced in the cicuit when the ate of change of cuent is /s. When flow of cuent in the cicuit stats, induced e.m.f. opposes this change. 6. n aveage induced e.m.f. of. V appeas in a coil when the cuent in it is changed fom 5. in one diection to 5. in the opposite diection in.s. Find the self-inductance of the coil. di Sol. veage dt di Using E L, dt. V L (5 /s) ( 5. ) (5.) 5 /s.s.v o, L 4.mH 5 / s MUTUL DUCTCE Conside two abitay conducting loops and. Suppose that is the instantaneous cuent flowing in loop. This cuent geneates a magnetic field B which links the second cicuit, giving ise to a magnetic flux though the second cicuit. Futhemoe, it is obvious that the flux though the second cicuit is zeo wheneve the cuent flowing aound the fist cicuit is zeo. t follows that the flux though the second cicuit is diectly popotional to the cuent flowing aound the fist cicuit. Hence,we can wite M whee the constant of popotionality M is called the mutual inductance of cicuit with espect to cicuit. Similaly, the flux though the fist cicuit due to the instantaneous cuent flowing aound the second cicuit is diectly popotional to that cuent, so we can wite M whee M is the mutual inductance of cicuit with espect to cicuit. t can be shown that M M. ote: M is a puely geometic quantity, depending only on the size, numbe of tuns, elative position and elative oientation of the two cicuits. The S.. unit of mutual inductance is called Heny (H). One heny is equal to a volt-second pe ampee. Suppose that the cuent flowing aound cicuit changes by an amount in a small time inteval t. The flux linking cicuit changes by an amount M in the same time inteval. ccoding to Faaday s law, an e.m.f. E t is geneated aound the second cicuit due to the changing magnetic flux linking that cicuit, Since, M, this e.m.f. can also be witten E M t Thus, the emf geneated aound the second cicuit due to the cuent flowing aound the fist cicuit is diectly popotional to the ate at which that cuent changes. Likewise, if the cuent flowing aound the second cicuit changes by an amount in a time inteval t then the e.m.f. geneated aound the fist cicuit is E M. t ote that thee is no diect physical connection (coupling) between the two cicuits the coupling is due entiely due to the magnetic field geneated by the cuents flowing aound the cicuits. 7. Two conducting cicula loops of adii and ae placed in the same plane with thei centes coinciding. Find the mutual inductance between them assuming <<. Sol. Suppose a cuent i is established in the oute loop. The magnetic field at the cente will be : i B s the adius of the inne coil is small compaed to, the flux of magnetic field though it will be appoximately i So that the mutual inductance is M TSFOME o i t is a device which aises o lowes the voltage in C cicuits though mutual induction. t consists of two coils wound on the same coe. The coil which is connected to the souce (i.e. to which input is applied) is called pimay coil while the othe which is connected to the load (i.e. fom which output is taken) is called seconday coil. The altenating cuent passing though the pimay coil ceates a continuously changing flux though the coe. This changing flux induces an altenating e.m.f. in the seconday coil. s magnetic lines of foce ae closed cuves, the flux pe tun of the pimay must be equal to the flux pe tun of the seconday coil. JSO STGE-_GE # 9

12 s p and p s. Thus, a V input at will step-up to 44 V output at 5.. (b) Step down Tansfome : f the seconday coil has less numbe of tuns than the pimay ( s < p ), the voltage is stepped down (V s < V p ). This type of aangement is called a stepdown tansfome. n this aangement, cuent in the seconday coil is moe inceased than in the pimay ( p / s < and s > p ). and S ae the flux passing though the pimay and seconday coils, and S ae the numbe of the tuns in pimay and seconday coils espectively, then, S S The numbe of tuns in each coil is constant, if d and d S ae the changes in flux in time dt in pimay and seconday coils espectively, then, o d dt d dt S E E S S S d as E dt nd as in an ideal tansfome thee is no loss of powe, so E constant, theefoe E E S TYES OF TSFOME S Tansfome can be divided mainly into two types: (a) Step up tansfome (a) Step up tansfome : S (b) Step down tansfome f the seconday coil has a geate numbe of tuns than the pimay ( s > p ), the voltage is stepped up (V s > V p ). This type of aangement is called a step-up tansfome. n this aangement, thee is less cuent in the seconday than in the pimay ( p / s < and s < p ). Eg.: f the pimay coil of a tansfome has tuns an the seconday has tuns, then Efficiency of Tansfome : Efficiency of tansfome, owe output owe input OTE : % o i egading a tansfome it is woth noting that : (i) t woks on C only and neve on DC (ii) t can incease o decease eithe voltage o cuent but not both simultaneously (as powe constant). (iii) Some powe is always lost due to flux leakage, hysteesis, eddy cuents, humming and heating of coils. 8. step-down tansfome convets a supply line voltage of volt into volt. The pimay coil has 5 tuns. The efficiency and powe tansmitted by the tansfome ae 9% and 8 kilowatt espectively. Calculate the numbe of tuns in the seconday coil. Sol. e e s p s p s p s 5 9. The pimay winding of a tansfome has 5 tuns wheeas its seconday has 5 tuns. The pimay is connected to an C supply of V, 5 Hz. What will be output of seconday coil? Sol. We know that S E S o E o E s E S 5 V Fequency emains same. GEETO This is a device which convet mechanical enegy into electical enegy using the pinciple of electomagnetic induction. t is of two types : JSO STGE-_GE #

13 (a) C Geneato o Dynamo : When a coil (conducto) is otated in a magnetic field, the magnetic flux linked with it changes and theefoe an altenating e.m.f. is induced in the coil. Constuction : The main pats of a dynamo ae:- (i) Field magnets : t is a stong hose shoe pemanent magnet. n electomagnet un by a DC souce can also be used fo high powe geneatos. (ii) matue : t is a soft ion coe on which a coil BCD having a lage numbe of tuns of insulated coppe wie is wound. This amatue (o coil) is otated apidly in the magnetic field between the poles of the magnet. (iii) Slip ings : The ends of the amatue (o the coil) ae connected to two coaxial metallic slip ings S and S which otate along with the coil. (iv) Bushes : Two bushes B and B made of cabon, pess against the slip ings S and S espectively. The extenal cicuit (i.e. load) is connected between the othe ends of bushes. The bushes B and B do not otate along with the coil. Woking of an C geneato : Suppose that the geneato coil BCD is initially in the hoizontal position. gain suppose that the coil BCD is being otated in the anticlockwise diection between the poles and S of a hose-shoe type magnet. (i) s the coil otates in the anticlockwise diection, the side B of the coil moves down cutting the magnetic lines of foce nea the -pole of the magnet and side CD moves up, cutting the lines of foce nea the S-pole of the magnet. Due to this, induced cuent is poduced in the sides B and DC of the coil. On applying Fleming s ight-hand ule to the sides B and DC of the coil, we find that the cuents ae in the diections B to and D to C. Thus, the induced cuents in the two sides of the coil ae in the same diection and we get an effective induced cuent in the diection BDC. (ii) fte half evolution, the sides B and DC of the coil will intechange thei positions. The side B will come on the ight hand side and side DC will come on the left hand side. So, afte half a evolution, side B stats moving up and side DC stats moving down. s a esult of this, the diection of induced cuent in each side of the coil is evesed afte half a evolution. Since the diection of induced cuent in the coil is evesed afte half evolution so that polaity (positive and negative) of the two ends of the coil also changes afte half evolution. The end of coil which was positive in the fist half of otation becomes negative in the second half. nd the end which was negative in the fist-half evolution becomes positive in the second half of evolution. Thus, in evolution of the coil, the cuent changes its diection times. The altenating cuent (C ) poduced in ndia has a fequency of 5 Hz. That is, the coil is otated at the ate of 5 evolutions pe second. Since in evolution of coil, the cuent changes its diection times, so in 5 evolutions of coil, the cuent changes its diection 5 times. Thus, the C supply in ndia changes its diection times in second. nothe way of saying this is that the altenating cuent poduced in ndia changes its diection evey / second. That is, each teminal of the coil is positive (+) fo / of a second and negative (-) fo the next / of a second. fte evey half evolution, each side of the geneato coil stats moving in the opposite diection in the magnetic field. The side of the coil which was initially moving upwads, afte half evolution, it stats moving downwads. Due to the change in the diection of motion of the two sides of the coil in the magnetic field afte evey half evolution, the diection of cuent poduced in them also changes afte evey half evolution. (b) DC Geneato (o DC Dynamo) : DC geneato means Diect Cuent geneato. That is, a DC geneato poduces diect cuent. Constuction of a DC Geneato : simple DC geneato consists of a ectangula coil BCD which can be otated apidly between the poles noth and south of a stong hoseshoe type magnet M. The geneato coil is made of a lage numbe of tuns of insulated coppe wie. The two ends of the coil ae connected to the two coppe half ings (o split ings) and of a commutato. Thee ae two cabon bushes B and B which pess lightly against the two half ings. When the coil is otated, the two half ings and touch the two cabon bushes B and B one by one. So, the cuent poduced in the otating coil can be tapped out though the commutato half ings into the cabon bushes. Fom the cabon bushes B and B, we can take the cuent into the vaious electical appliances like adio, T.V., electic ion, bulbs, etc. JSO STGE-_GE #

14 Commutato (Split ing) Cabon emanent bushes magnet ntclockwise + Woking of a DC geneato : B B y Load D.C. VVVV ectangula Coil D.C. otation Geneato of coil anticlockwise Suppose that the geneato coil BCD is initially in the hoizontal position. gain suppose that the coil BCD is being otated in the anticlockwise diection between the poles and S of a hoseshoes type magnet. (i) s the coil otates in the anticlockwise diection, the side B of the coil moves down cutting the magnetic lines of foce nea the -pole of the magnet and side DC moves up, cutting the lines of foce nea the S-pole of the magnet in figue. Due to this, induced cuent is poduced in the sides B and DC of the coil. On applying Fleming s ight-hand ule to the sides B and DC of the coil we find that the cuents in them ae in the diections B to and D to C espectively. Thus, we get an effective induced cuent in the diection BDC. Due to this the bush B becomes a positive (+) pole and bush B becomes negative (-) pole of the geneato. (ii) fte half evolution the sides B and DC of the coil will intechange thei positions. The side B will come on the ight hand side and stat moving up wheeas side DC will come on the left-hand side and stat moving down. But when sides of the coil intechange thei positions, then the two commutato half ings and automatically change thei contacts fom one cabon bush to the othe. Due to this change, the cuent keeps flowing in the same diection in the cicuit. The bush B will always emain positive teminal and bush B will always emain negative teminal of the geneato. Thus, a DC geneato supplies a cuent in one diection by the use of a commutato consisting of two half-ings of coppe. Diffeence between a DC geneato and an C geneato : n a DC geneato we connect the two ends of the coil to a commutato consisting of two, half ings of coppe. On the othe hand, in an C geneato, we connect the two ends of the coil to two full ings of coppe called slip ings. ELECTC MOTO moto is a device which convets electical enegy into mechanical enegy. Evey moto has a shaft o spindle which otates continuously when cuent is passed into it. The otation of its shafts is used to dive the vaious types of machines in homes and industy. Electic moto is used in electic fans, washing machines, efigeatos, mixe and ginde and many othe appliances. common electic moto woks on diect cuent. So, it is also called DC moto, which means a Diect Cuent moto. The electic moto which we ae going to discuss now is actually a DC moto. (a) inciple of a Moto : n electic moto utilizes the magnetic effect of cuent. moto woks on the pinciple that when a ectangula coil is placed in a magnetic field and cuent is passed though it, a toque acts on the coil which otates it continuously. When the coil otates, the shaft attached to it also otates. n this way the electical enegy supplied to the moto is conveted into the mechanical enegy of otation. (b) Constuction of a Moto : n electic moto consists of a ectangula coil BCD of insulated coppe wie, wound on a soft ion coe called amatue. The soft ion coe has not been shown in figue to make things simple. The coil is mounted between the cuved poles of a U-shaped pemanent magnet in such a way that it can otate between the poles and S. The two ends of the coil ae soldeed (o welded) pemanently to the two half ings X and Y of a commutato. Commutato (Split ing) Cabon emanent bushes magnet ntclockwise F F + y ectangula Battey Coil n electic otation moto of coil anticlockwise commutato is a coppe ing split into two pats X and Y, these two pats ae insulated fom one anothe and mounted on the shaft of the moto. End of the coil is welded to pat X of the commutato and end D of the coil is welded to pat Y of the commutato. The commutato ings ae mounted on Q JSO STGE-_GE #

15 the shaft of the coil and they also otate when the coil otates. The function of commutato ings is to evese the diection of cuent flowing though the coil evey time the coil just passes the vetical position duing a evolution. We cannot join the battey wies diectly to the two commutato s half ings to pass cuent into the coil because if we do so, then the connecting wies will get twisted when the coil otates. So, to pass the electic cuent to the coil, we use two cabon stips and Q known as bushes. The cabon bushes and Q ae fixed to the base of the moto and they pess lightly against the two half ings of the commutato. The function of cabon bushes is to make contact with the otating ings of the commutato and though them to supply cuent to the coil. t should be noted that any one bush touches only one ing at a time, so that when the coil otates, the two bushes will touch both the ings one by one. (c) Woking of a Moto : Suppose that initially the coil BCD is in the hoizontal position as shown in figue. On pessing the switch, the cuent entes the coil though cabon bush and commutato half ing X. The cuent flows in the diection BCD and leaves via ing Y and bush Q. (i) n side B of the coil, the diection of cuent is fom to B and the diection of magnetic field is fom to S pole. So, by applying Fleming s left hand ule to the side B of the coil we find that it will expeience a foce in the upwad diection. (ii) n side DC of the coil, the diection of cuent is fom C to D towads but the diection of magnetic field emains the same fom to S pole as shown in figue. So, by applying Fleming s left hand ule to the side DC of the coil, we find that. t will expeience a foce in the downwad diection. (iii) We find that the foce acting on the side B of the coil is in the upwad diection wheeas the foce acting on the side DC of the coil is in the downwad diection. These two equal, opposite and paallel foces acting on the two sides of the coil fom a couple (toque) and otate the coil in the anticlockwise diection. (iv) While otating, when the coil eaches the vetical position, then the bushes and Q will touch the gap between the two commutato ings and cuent to the coil is cut off. Though the cuent to the coil is cut off when it is in the exact vetical position, the coil doesn t stop otating because it has aleady gained momentum due to which it goes beyond the vetical position. (v) When the coil goes beyond the vetical position, the two commutato s half ings automatically change contact fom one bush to the othe. This eveses the diection of cuent though the coil which, in tun, eveses the diection of foces acting on the two sides of the coil. The side B of the coil will now be on the left hand side with a downwad foce on it, wheeas side DC of the coil will come on the ight hand side with an upwad foce on it. n this position also a couple acts on the coil which otates it in the same diection (anticlockwise diection). This pocess is epeated again and again and the coil continues to otate as long as the cuent is passing. This is how an electic moto woks. JSO STGE-_GE # 3

16 ELECTCTY COSEVTO OF ELECTC CHGE Wheneve two bodies ae chaged by ubbing, one gets positively chaged and the othe gets negatively chaged. The net chage on the two bodies, howeve, emains zeo the same as that befoe ubbing. n othe wods, chage is conseved. t can neithe be ceated no be destoyed. The only thing that happens on ubbing is that chaged paticles (electons) get tansfeed fom one body to the othe. n some phenomena, chaged paticles ae ceated. But even then the consevation of chage holds. Fo example, a fee neuton convets itself into an electon and the poton taken togethe is also zeo. So, thee is no change in the convesion of a neuton to an electon and a poton. COULOMB S LW Chales ugustine de Coulomb studied the inteaction foces of chaged paticles in detail in 784. He used a tosion balance. On the basis of his expeiments he established Coulomb s law. ccoding to this law the magnitude of the electic foce between two point chages is diectly popotional to the poduct of the magnitude of the two chages and invesely popotional to the squae of the distance between them and acts along the staight line joining the two chages. n mathematical tems, the foce that each of the two point chages q and q at a distance apat exets on the othe can be expessed as qq F k This foce is epulsive fo like chages and attactive fo unlike chages. Whee k is a constant of popotionality. k 4, hee is absolute pemittivity of fee space. The foce is diected along the line joining the centes of the two chaged paticles. Fo any othe medium except ai, fee space o vacuum coulomb s law educes to F q q 4 emittivity of the medium and elative emittivity o dielectic constant of the medium. Coulomb s law is based on physical obsevation and it is not logically deived fom any othe concept. LLUSTTOS. Find out the electostatics foce between two point chages placed in ai (each of + C) if they ae sepaated by m. kqq Sol. F e ote : Fom the above esult we can say that C chage is too lage to ealize. n natue, chage is usually of the ode of C. paticle of mass m caying chage q is evolving aound a fixed chage q in a cicula path of adius. Calculate the peiod of evolution and its speed also. Sol. qq 4 T o 4 m m ' T q q ( 4 ) (4 m) T 4 q q m and also we can say that q q 4 mv V qq 4 m OETES OF ELECTC FELD TESTY (i) t is a vecto quantity. ts diection is the same as the foce expeienced by positive chage. (ii) Electic field due to positive chage is always away fom it while due to negative chage always towads it. (iii) ts S.. unit is ewton/coulomb. (iv) Electic foce on a chage q placed in a egion of electic field at a point whee the electic field intensity is E is given by F qe. Electic foce on point chage is in the same diection of electic field on positive chage and in opposite diection on a negative chage. (v) t obeys the supeposition pinciple, that is, the field intensity at a point due to a system of chages is vecto sum of the field intensities due to individual JSO STGE-_GE # 4

17 point chages. E E E E (vi) t is poduced by souce chages. The electic field will be a fixed value at a point unless we change the distibution of souce chages. 3. Five point chages, each of value q ae placed on five vetices of a egula hexagon of side L. What is the magnitude of the foce on a point chage of value q coulomb placed at the cente of the hexagon? F q E q Sol. f thee had been a sixth chage +q at the emaining vetex of hexagon foce due to all the six chages on q at O would be zeo (as the foces due to individual chages will balance each othe), i.e., L O -q F ow if f is the foce due to sixth chage and F due to emaining five chages. F + f i.e. F f o, F f q q 4 L q D q B q q 4 L C Sol. s foce on a chage q in an electic field E is F q q E So accoding to given poblem F W i.e., q E mg q i.e., E mg q W /C., in downwad diection. ELECTOSTTC EQULBUM The position whee the esultant foce on a chaged paticle becomes zeo is called equilibium position. (a) Stable Equilibium : chage is initially in equilibium position and is displaced by a small distance. f the chage ties to etun back to the same equilibium position then this equilibium is called position of stable equilibium. (b) Unstable Equilibium : f chage is displaced by a small distance fom its equilibium position and the chage has no tendency to etun to the same equilibium position. nstead it goes away fom the equilibium position. (c) eutal Equilibium : f chage is displaced by a small distance and it is still in equilibium condition then it is called neutal equilibium. 5. Two equal positive point chages 'Q' ae fixed at points B(a, ) and ( a, ). nothe test chage q is also placed at O(, ). Show that the equilibium at 'O' is (i) stable fo displacement along X-axis. (ii) unstable fo displacement along Y-axis. F e q E F et F q CO 4 L along CO Sol. (i) 4. Calculate the electic field intensity which would be just sufficient to balance the weight of a paticle of chage c and mass mg. nitially F O F KQq FO FBO a + BO When chage is slightly shifted towads + x axis by a small distance x, then. FO < FBO JSO STGE-_GE # 5

18 Theefoe the paticle will move towads oigin (its oiginal position) hence the equilibium is stable. (ii) When chage is shifted along y axis fte esolving components net foce will be along y axis so the paticle will not etun to its oiginal position so it is unstable equilibium. Finally the chage will move to infinity. ELECTC LES OF FOCE (ELOF) The line of foce in an electic field is an imaginay line, the tangent to which at any point on it epesents the diection of electic field at the given point. (a) opeties : (i) Line of foce oiginates out fom a positive chage and teminates on a negative chage. f thee is only one positive chage then lines stat fom positive chage and teminate at. f thee is only one negative chage then lines stat fom and teminates at negative chage. (ii) The electic intensity at a point is the numbe of lines of foce steaming though pe unit aea nomal to the diection of the intensity at that point. The intensity will be moe whee the density of lines is moe. (iii) umbe of lines oiginating (teminating) fom (on) is diectly popotional to the magnitude of the chage. (iv) ELOF of esultant electic field can neve intesect with each othe. (v) Electic lines of foce poduced by static chages do not fom close loop. ( vi) Elec tic lines of foce end o stat pependiculaly on the suface of a conducto. (vii) Electic lines of foce neve ente into conductos. 6. f numbe of electic lines of foce fom chage q ae then find out numbe of electic lines of foce fom q chage. Sol. o. of ELOF chage q q So numbe of ELOF will be. 7. chage + Q is fixed at a distance of d in font of an infinite metal plate. Daw the lines of foce indicating the diections clealy. JSO STGE-_GE # 6

19 Sol. Thee will be induced chage on two sufaces of conducting plate, so ELOF will stat fom +Q chage and teminate at conducto and then will again stat fom othe suface of conducto. ELECTC FLUX Conside some suface in an electic field E. Let us select a small aea element ds The electic flux of the field ove the aea element is given by d E Diection of ds nˆ o o o d E EdS cos d E (E cos ) ds d E E n ds E. ds on this suface. is nomal to the suface. t is along ds whee E n is the component of electic field in the diection of ds. f the electic field is unifom ove that aea then E E S (a) hysical Meaning : The electic flux though a suface inside an electic field epesents the total numbe of electic lines of foce cossing the suface in a diection nomal the suface. t is a popety of electic field (b) Unit : (i) The S unit of electic flux is m C (gauss) o J m C. (ii) Electic flux is a scala quantity. (t can be positive, negative o zeo) 8. The electic field in a egion is given by, 3 4 E E i E j with E. 3 /C. Find the 5 5 flux of this field though a ectangula suface of aea.m paallel to the Y Z plane. Sol. E E S 3 4 E i E j 5 5..î 4 E m C ELECTCL ESSTCE The popety of a substance by vitue of which it opposes the flow of electic cuent though it is temed as electical esistance. Electical esistance depends on the size, geomety, tempeatue and intenal stuctue of the conducto. We known that, v d ev m nev d ne ne V m V m ne V m ne m ne m ne ee m ev m is called esistivity (it is also called specific esistance), and m ne, is called conductivity. Theefoe cuent in conductos is popotional to potential diffeence applied acoss its ends. This is Ohm's Law. Units: m also called siemens m. 9. f a coppe wie is stetched to make its adius decease by.5%, Find the pecentage incease in esistance (appoximately). Sol. Due to stetching esistance changes ae in the atio o o %.6% JSO STGE-_GE # 7

20 EFFECT OF STETCHG OF WE O ESSTCE n stetching, the density of wie usually does not change. Theefoe Volume befoe stetching Volume afte stetching and f infomation of lengths befoe and afte stetching is given, then use f infomation of adius and is given then use 4 This constant f ohm, t C, then t Thus, the tempeatue coefficient of esistance is equal to the incease in esistance of a conducto having a esistance of one ohm on aising its tempeatue by C. The tempeatue coefficient of esistance may be positive o negative. Fom calculations it is found that fo most of the metals the value of is nealy / 73 substituting in the above equation t 73 t 73 t 73 T 73 C. Hence whee T is the absolute tempeatue of the conducto. t T Thus, the esistance of a pue metallic wie is diectly popotional to its absolute tempeatue. The gaph dawn between the esistance t and tempeatue t is found to be a staight line CODUCTVTY : (a) ecipocal of esistivity of a conducto is called its conductivity. t is geneally epesented by. t (b) tºc (c) Unit : ohm. mete EFFECT OF TEMETUE O ESSTCE D ESSTVTY The esistance of a conducto depends upon the tempeatue. s the tempeatue inceases, the andom motion of fee electons also inceases. f the numbe density of chage caie electons emains constant as in the case of a conducto, then the incease of andom motion inceases the esistivity. The vaiation of esistance with tempeatue is given by the following elation t t whee t and ae the esistance at t C and C espectively and is called as tempeatue coefficient of esistance of the substance. o t t The esistivity o specific esistance vaies with tempeatue. This vaiation is due to change in esistance of a conducto with tempeatue. The dependence of the esistivity with tempeatue is epesented by the following equation. t t With the ise of tempeatue the specific esistance o esistivity of pue metals inceases and that of semi-conductos and insulatos decease. The esistivity of alloys inceases with the ise of tempeatue but less than that of metals. On applying pessue on pue metals, its esistivity deceases but on applying tension, the esistivity inceases. The esistance of alloys such as eueka, manganin etc., inceases in smalle amount with the ise in tempeatue. Thei tempeatue coefficient of esistance is negligible. On account of thei high esistivity and negligible tempeatue coefficient of esistance these alloys ae used to make wies fo esistance boxes, potentiomete, mete bidge etc., The esistance of semiconductos, insulatos, JSO STGE-_GE # 8

21 electolytes etc., deceases with the ise in tempeatue. Thei tempeatue coefficients of esistance ae negative. On inceasing the tempeatue of semi conductos a lage numbe of electons get fee afte beaking thei bonds. These electons each the conduction band fom valence band. Thus conductivity inceases o esistivity deceases with the incease of fee electon density.. wie has a esistance of ohm at 73 K and a esistance of.5 ohm at 373 K. What is the tempeatue coefficient of esistance of the mateial? The aangement of Wheatstone bidge is shown in figue below. Out of fou esistos, two esistances, and 3, 4 ae connected in seies and ae joined in paallel acoss two points a and c. battey of emf E is connected acoss junctions a and c and a galvanomete (G) between junction b and d. The keys K and K ae used fo the flow of cuent in the vaious banches of bidge. inciple of Wheatstone Bidge : When key K is closed, cuent i fom the battey is divided at junction a in two pats. pat i goes though and the est i goes though 3. When key K is closed, galvanomete shows a deflection..5 Sol. T T / K SUE CODUCTO D TS LCTOS of. K. Onnes in 9 discoveed that cetain metals and alloys at vey low tempeatue lose thei esistance consideably. This phenomenon is known as supe-conductivity. s the tempeatue deceases, the esistance of the mateial also deceases, but when the tempeatue eaches a cetain citical value (called citical tempeatue o tansition tempeatue), the esistance of the mateial completely disappeas i.e. it becomes zeo. Then the mateial behaves as if it is a supe-conducto and thee will be flow of electons without any esistance whatsoeve. The citical tempeatue is diffeent fo diffeent mateial. t has been found that mecuy at citical tempeatue 4. K, lead at 7.5 K and niobium at citical tempeatue 9. K become supe-conducto. pplications of supe conductos : (i) Supe conductos ae used fo making vey stong electomagnets. (ii) Supe conductivity is playing an impotant ole in mateial science eseach and high enegy paticle physics. (iii) Supe conductivity is used to poduce vey high speed computes. (iv) Supe conductos ae used fo the tansmission of electic powe. WHETSTOE BDGE Wheatstone bidge is an aangement of fou esistos in the shape of a quadilateal which can be used to measue unknown esistance in tems of the emaining thee esistances. The diection of deflection depends on the value of potential diffeence between b and d. When the value of potential at b and d is same, then no cuent will flow though galvanomete. This condition is known as the condition of balanced bidge o null deflection condition. This situation can be obtained by choosing suitable values of the esistances. Thus, in null deflection state, we have : V a V b V a V d o i i 3...(i) Similaly : V b V c V d V c o i i 4...(ii) On dividing equation (i) by (ii), we get i i i i 3 4 o 3...(iii) 4 Equation (iii) states the condition of balanced bidge. Thus, in null deflection condition the atio of esistances of adjacent ams of the bidge ae same. The esisto of unknown esistance is usually connected in one of the am of the bidge. The esistance of one of the emaining thee ams is adjusted such that the galvanomete shows zeo deflection. f esistance of unknown esisto is 4. Then 4 ( 3 ) Fo bette accuacy of the bidge one should choose esistances,, 3 and 4 of same ode. JSO STGE-_GE # 9

22 KCHHOFF'S LWS (a) Kichhoff s Cuent Law (Junction law) : This law is based on law of consevation of chage. t states that "The algebaic sum of the cuents meeting at a point of the cicuit is zeo" o total cuent enteing a junction is equal total cuent leaving the junction. in out. t is also known as KCL (Kichhoff's cuent law). ( b) Kichhof f s Voltage Law (Loop law) : The algebaic sum of all the potential diffeences along a closed loop is zeo. + EMF. The closed loop can be tavesed in any diection. While tavesing a loop if potential inceases, put a positive sign in expession and if potential deceases put a negative sign. Sol. pplying KVL in loop CEFDC 5 i i i 5 C 5V i i E V V + V 3 V 4. Boxes may contain esisto o battey o any othe element (linea o nonlinea). t is also known as KVL. Figue shows, cuent in a pat of electical cicuit, what will be the value of cuent (i)? Sol. Q S 3 3 i Q i i i 3.3 S i.3 Fom KCL, cuent at junction, i Fom KCL, cuent at junction Q, i i Fom KCL, cuent at junction, i 3 i 6 4 Fom KCL, cuent at junction S, i i n the cicuit shown, calculate the value of in ohm that will esult in no cuent though the 3 V battey. B otential dop acoss otential dop acoss B i GOUG OF CELLS (a) Cells in Seies : E, E, E 3, E 3 n n E eq,eq B Equivalent EMF E eq E + E E n (wite EMF s with polaity) Equivalent intenal esistance eq n f n cells each of emf E, ae aanged in seies and if is intenal esistance of each cell, then total emf ne E, E, E, E, D Upto n ne So cuent in the cicuit, n Thee may by two cases : (i) f n <<, then ne n cuent due to one cell. B B i F So, seies combination is advantageous. JSO STGE-_GE #