RJC 2017 16 Electromagnetism notes

se©¥ection for charged partic©¥es. ţ (m ) explain how e©¥ectric and m agnetic fields can be used in velocity uniform electric and uniform m agnetic fie©¥ds. [ ćļyjjabū¡½ (I) describe and analyse def©¥ections of beam s f©¥m©¥es by (k) recall and solve problem s using F = B Q v sin 6 . ©¤ ü) predict the direction of the force on a charge m oving in a m agnetic the direction of the forces. (i) explain the forces between current - carrying conductors and predict using a current balance. conductor can be used to m easure the flux density of a m agnetic fie©¥d (h) show an understanding of how the force on a current - c a iT ying (g) defl e m agnetic f©¥ux density and the tesla. directions as interpreted by F lem ing ' s le ft - hand ru©¥e . (f) recall and so©¥ve problem s using the equation F = B IL sin Q , w ith m agnetic field m ight experience a force. (e) show an understanding that a current - c a r r ying conductor p©¥aced in a be inf©¥uenced by the presence of feiT ous core . (d) show an understanding that the m agnetic fie©¥d due to a solenoid m ay ©¥ong so©¥enoid respectively . fields due to ' currents in a long straight w ire, a f©¥at circular coil and a 2 trd 2 r use B - , B - / ©¥oN l and B ¡¤ llonl for the f©¥ux densities of the (c) circular coi©¥ and a long solenoid . (b) sketch flux patterns due to currents in a ©¥ong etralght w ire , a ¨¤at perm anent m agnets. of force produced either by current - c a r r ying conductora or by (a) show an understanding that a m agnetic field ©¥a an exam ple of a fie©¥d C andldales shou©¥d be able to üÞ L oarnlng O utcom o8 F o r ce on a mo v i ng ch a r ge I Not In H1 ryllabusl * F o rce b e tw e e n cu rre nt - c a r r ying conductors F o r ce on a currenlarrying conductor * M a g n e tic fie ld s d u e I o c u rre n ©¥s C o n c ep t of a ma g n e t ic fie©¥d ¨¡ntent

are produced by static charqes. experienced by mo v ©¥n g à¤画 as opposed to elė ctń ç lields, w hich It is ©¥m portant to note that m agnetic fields are produced and flux density is a A m agnetic field is a region of space w here a m agnetic pole the other. the interaction be©¥w een one m agnet and the m agnetic field of o T he force exerted by one m agnet on another m agnet is due to A m agnet sets up a m agnetic field in its vicinity . m agnetic field m agnetic field. C oncept of a F orces betw een m agnets can be explained using the concept of a ņ the m agnet and the other the south po©¥e. (v) T he pole that points tow ards the north is called the north pole of the E arth ' s N orth - S outh axis. align so that the line joining its poles is approxim ately parallel to (iv) W hen no other m agnet is near, a * eely suspended m agnet w i©¥©¥ (iii) P o©¥es occur in equal and opposite pairs (dipoles) . Oi) Like poles repel each other, u n like poles attract. (i) M agnetic poles are of 2 kinds : N orth (N ) or S outh (S ) E xperim ents have shown that m agnet called poles. T h e ma gn e tic pr op e r ties of a ma gn et or igi na te at cer tai n reg i on s in the the nam e of one of thė locations these stones w ere found. sites m ore than tw o thousand years o©¥d. T he term ' m a gneť com es from m agnets ¡¤ N atu ra l m ag n e ts h ave be e n d isco ve re d fro m a n cie nt a rcha e o log ica l P roperties of 16 . 1 C oncer¨¡ of a m B Įtietic field Y 54 P H Y S ©¥C S D E P A R T M E N T R A F F L E S ©¥N S T ©¥T U T ©¥O N 2 0 17

uniform field c«»nstant, 1. e . a 1 P ©¥ines B ©¥s r a f al lel tie©¥d n - force that acts on the north m agnetic pole of a m agnet. T his is because the direction of the field ls given by the direction of the the arrow s point aw ay from the\N # O ©¥ö of ā m agnet tow ard the S ii©¢©¢ M agnitude of ©¬, \ ©¥f th ìÚ Field is uniform , the field lines are evenly spaced, t he \ nufnber of lined per unit cross- s ectional area lstproporl¢çm l to the and t heängentlto a field ©¥ine at a point gives thep©¥rectloitof B at that point, (a) B ar m agnet F ig . 3 F ig . 2 t P the plane of the paper respective©¥y . and crosses, depending on w hether it is perpendicularly pointing out or into F or a tw o - dim ensiona©¥ view , m a gnetic fields can be represented by dots F lg . 1 (a) non - uniform field (b) uniform field together = > B large 1Óö F ie©¥d ©¥ines close B sm a©¥©¥ r= Į ©¥= i Jp of B at P * D irect©¥on üÞ 国 field of a m agnetic R epresentation A m agnetic field can be represented by field lines draw n such that Y 5 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S ©¥N S T IT U T IO N 20 17

4 horizontal plane are affected only by B H ¡¤ Instrum ents sucH as com pass needles w hose m otion is confined in a m = B E ©¥M S iri¨¡ IB H = B . C OF orm ula ņ It is convenient to resolve ©¬E arth in to h o rizo n ta l a n d ve rtica l co m p o ne nts . angle of incliiTalion, a ) » om the horizontal. A t al©¥ other positions, the B E . rth is inclined at various angles (called the m agnetic field, ©¬E , rth, is alm ost horizontal. F rom the field pattern, it can be seen that, n e a r the equator, the E arth ' s geographical to the south of a bar m agnet) . N o©¥lh pole (because the north end of a com pass need©¥e l8 attracted T he north of a com pass needle points tow ards the E arth ' 8 m a gnetic inside the centre of the E arth. T he fie©¥d pattern l8 sim ilar to that of a bar m agnet em bedded deep N orth does not coincide exactly w ith the m agnetic N orth. ti©¥ted 1 1 ¡Æ w ith re s p e c t to lts ro ta tio n a l a x is . H ence, the geographica©¥ ©¥t ls know n that the ax©¥s of the E arth ' 8 magnuc fie©¥d ls approx©¥m ate©¥y E arth ' 8 s u rface and changes gradua©¥©¥y w ith tim e. T he m agnitude and direction of lhls field varies w llh position over the caused by e©¥ectrlc currents clrcu©¥aling w ithin the core of the E arth, T he E arth ' 8 m a gnetic fie©¥d ©¥e ' a w e a k m agnetic fie©¥d believed to be Y ØßÙ£ P H Y S IC S D E P A R T M E N T R A F F L E S ©¥N S T ©¥T U T ©¥O N 20 17 field ' E a rth ' s m a g n e t©¥c .

5 3 \ dlt c \ - + d©¥JtÀnĹ f \ Qltļ the current w hich flows through it. relationship betw een the m agnetic field of a current carrying conductor and F o©¥low ing O ersteď s discovery, e x perim ents deduced that there is a surrounds it can be seen. of the m agnetic fle©¥d w hich carrying conductor, the pattern com passes around the current - B y arranging an assortm ent of opposite direction. needle w ould deflect in the of the sam e conductor, the W hen aligned on the other side def©¥ected in one way . conductor, the needle w ould be side of a current - carrying com pass w as aligned on one It w as found that w hen a 囤 electric current. H is findings saw the birth of electrom agnetism . In 1 8 1 9 , H ans C hristian O ersted discovered the m agnetic effect of an e lectrom ag n etis m T he birth of 1 6 . 2 agnetic fields due to currents F ig . 5 x = n e u tra ©¥ p o in t a bar m agnet. (b) E ffect of E arth ' s field on that ofhorizontal plane (a) E arth ' s ©¥oca©¥ field in a A 4 ¡½ ½Ã 亲 üÞ pointing N . T he crosses indicate neutral poĺnts w here the resultant field is show s the com bined field due to the E arth and a bar m agnet w ith its N pole F ig . 5 (a) show s the E arth ' s local field in a horizontal plane and F ig , 5 (b) lines are parallel, e qually spaced and point due north, L ocally, the E arth ' s m a gnetic field ' c a n be considered as a uniform field ; the Y 5 4 P H Y S ©¥C S D E P A R T M E N T R A F F L E S IN S T ©¥T U T ©¥O N 2 0 17

I ¡¤ c u rre n t in th e w ire w here B ¡¤ m ag ne tic flux d e n sity the w ire is directed into the paper and its m agnitude is given by paper. A t the point P , the m agnetic flux density due to the current in F ig . 8 show s an infinite©¥y long straight w ire ©¥ying in the plane of the Fig . a It [s assigned a value of 4 n x 1 0 4 H m 1 . » ee space (vacuum ) , po ¡¤ a co n sta n