Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

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Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets.

One pole calle oth () an othe pole calle outh () Opposite poles attact Like poles epels Chapte 8: Magnetic fiels If the ba magnet

magnetic poles ae always foun in pais, we cannot isolate fom Cut in two pieces Chapte 8: Magnetic iel an Magnetic oce Like E-fiel,

These lines epesent the iection of foce that woul exet on pieces of ion Magnetic fiel lines can be tace by the ai of compass o with

though a magnetic fiel, it will expeience a magnetic foce.

1 Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to non-equialent poles. One pole calle oth () an othe pole calle outh () Opposite poles attact Like poles epels Chapte 8: Magnetic fiels If the ba magnet is suspene on a thea (like compass) pole seach geogaphic noth (eath magnetic pole) pole seach geogaphic south (eath magnetic pole) magnetic poles ae always foun in pais, we cannot isolate fom Cut in two pieces Chapte 8: Magnetic iel an Magnetic oce Like E-fiel, Magnets has a magnetic fiel ( - fiel) can be epesente by lines away fom - pole towas pole. These lines epesent the iection of foce that woul exet on pieces of ion Magnetic fiel lines can be tace by the ai of compass o with ion.(برادة حديد) fillings Analogous to electic ipole Chapte 8: Magnetic iel an Magnetic oce When a chage paticle moe with elocity though a magnetic fiel, it will expeience a magnetic foce. A seies of expeiements shows that q, ( =, ) // ( θ = 0 ) = 0 ( θ = 90 ) = max = q sinθ θ 0, q 0, -foce is popotional to q magnitue an its spee -foce is a funtion of elocity an -fiel (When paticle moes // -fiel) (Diection of -foce to an plane) ( < ) Opposite iection to ( q > 0, ) +q θ 1

Chapte 8: Magnetic iel an Magnetic oce = q Aboe esults can be summaize by: Magnitue of foce on moing chage paticle is = = q sinθ The iection of can be etemine using ight han ule thumb is in iection

m) Diection of foce on +e chage Diection of foce on -e chage Chapte 8: Magnetic iel an Magnetic oce: compaison between magnetic an electic foces If we compae between -foce an E-foce = q an = qe E

2 Chapte 8: Magnetic iel an Magnetic oce = q Aboe esults can be summaize by: Magnitue of foce on moing chage paticle is = = q sinθ The iection of can be etemine using ight han ule thumb is in iection of on +e chage thumb is opposite to the iection of on e chage The -fiel I unit is Tesla (T)=/(C.m/s)=/(A.m) Diection of foce on +e chage Diection of foce on -e chage Chapte 8: Magnetic iel an Magnetic oce: compaison between magnetic an electic foces If we compae between -foce an E-foce = q an = qe E E-foces act in the iection of the E-fiel, -foces ae pepenicula to the -fiel. A -foce exists only fo chages in motion. ut E-foce act on moing o steay chages The -foce of a steay magnetic fiel oes no wok when isplacing a chage paticle ( s). ut, E-foce o wok when isplacing chage paticle (E // s) The -fiel can alte the iection of a moing chage paticle but not its spee o its kinetic enegy. ut, E-fiel alte iection, spee o kinetic enegy of chage paticle. Chapte 8: Magnetic iel an Magnetic oce: Ex: An electon in TV moes towa sceen with a spee of m/s along the x Axis. uouning the neck of the tube ae coils of wie that ceate a magnetic fiel of magnitue 0.05 T, iecte at an angle of 60 to the x axis an lying in the xy plane. (A) Calculate the magnetic foce on the electon. () in a ecto expession fo the magnetic foce on the electon Chapte 8: Motion of chage paticle in a unifom magnetic fiel If we assume the plane of the page to be the xy plane, the pepenicula to the plane (z-iection) will be out of the page o into the page. imilaly, If the magnetic fiel out of the page, it can be epesente by ots ( ). If -fiel is into the page, it can be epesente by ( ) y ight han ule, thump is in +e z-iection on electon is in e z-iection

3 Chapte 8: Motion of chage paticle in a unifom magnetic fiel Consie a positie chage moing pepenicula to a magnetic fiel with an initial elocity,. The foce is always at ight angles to an its magnitue is, = q towas the cente o, as q moes, it will otate about a cicle an an will always be pepenicula. The magnitue of will always be the same, only its iection will change (unifom cicula motion). Chapte 8: Motion of chage paticle in a unifom magnetic fiel: the cycloton fequency To fin the aius an fequency of the otation: The aial foce = ma = q = m m = q q an = m (aius of otation) (chage spee) The angula spee q ω = = m (Cycloton fequency) The peio fo this otation (ewton n law in aial iection) π π πm T = = = ω q Chapte 8: Motion of chage paticle in a unifom magnetic fiel If makes an abitay angle (θ 90 ) with (in the x-iection) θ must be to x-axis no foce component in x-iection we hae only foce components in y an z iection a x =0 x = constant We hae a c ue to foce towas cente which changes between y an z y an z change in time The esulting motion is a helix Chapte 8: Motion of chage paticle in a unifom magnetic fiel Ex: A poton is moing in a cicula obit of aius 14 cm in a unifom 0.35-T magnetic fiel pepenicula to the elocity of the poton. in the spee of the poton. = q = m q = m The equations fo the cycloton fequency an otation peio still apply poie that eplace by = y + z 3

Chapte 8: Motion of chage paticle in a unifom magnetic fiel Ex: Electons ae acceleate fom est though a potential iffeence of 350 V. The electons tael along a cue path of aius 7.5 cm ue to - fiel.

me (A) = q = m = q To fin we may use conseation of enegy Chapte 8: Applications Inoling Chage Paticles Moing in a Magnetic iel If chage paticle moe une influence of E-fiel an -fiel it will be affecte

selecto application) om the expession () hown iections fo e an ae on +e chage paticle Chapte 8: Applications Inoling Chage Paticles Moing in a Magnetic iel Othe application inclues the sepaation of

4 Chapte 8: Motion of chage paticle in a unifom magnetic fiel Ex: Electons ae acceleate fom est though a potential iffeence of 350 V. The electons tael along a cue path of aius 7.5 cm ue to - fiel. If the magnetic fiel is pepenicula to the beam. (A) What is the magnitue of the magnetic fiel? () What is the angula spee of the electons? me (A) = q = m = q To fin we may use conseation of enegy Chapte 8: Applications Inoling Chage Paticles Moing in a Magnetic iel If chage paticle moe une influence of E-fiel an -fiel it will be affecte by both E an on it (Loentz foce): If both E an hae same magnitue but opposite iections as shown chage paticle will moe etically staight though the egion of fiels with constant elocity (elocity selecto application) om the expession () hown iections fo e an ae on +e chage paticle Chapte 8: Applications Inoling Chage Paticles Moing in a Magnetic iel Othe application inclues the sepaation of ions accoing to thei mass-to-chage atio (Mass pectomete eice). A beam of ions fist passes though a elocity selecto an then entes a secon aea of unifom magnetic fiel as shown when enteing, the ions moe in a semicicle of aius befoe stiking a etecto aay at P. m om eq. = q0 = m 0 = q m 0 E =, but = q = q E m 0 Chapte 8 Magnetic oce on a Cuent Caying Conucto o a conucto with cuent passing though it an place in a magnetic fiel Magnetic foce acts upon chages moing in a conucto. The total foce on the cuent is the integal sum of the foce on each chage in the cuent. In tun, the chages tansfe the foce on to the wie when they collie with the atoms of the wie. 4

Chapte 8 Magnetic oce on a Cuent Caying Conucto Chapte 8 Magnetic oce on a Cuent Caying

cuent I in a unifom magnetic fiel as in figue Vetical suspene wie between magnet poles

eflect to the left ( to the left) When I is ownwa wie eflect to the ight ( to the ight)

Insie the wie, a chages moe with along the length L will hae a magnetic foce, q o the

n = /V o a staight wie in a unifom -fiel.

Magnetic oce on a Cuent Caying Conucto If we consie an abitay shape wie of unifom coss

segment length ecto (s ) = Is Total foce acting on the wie will be: b = I s a o an abitay

a an b ae en points of the wie a b Chapte 8 Magnetic oce on a Cuent Caying Conucto o

5 Chapte 8 Magnetic oce on a Cuent Caying Conucto Chapte 8 Magnetic oce on a Cuent Caying Conucto consie a staight segment of wie of length L an coss-sectional aea A caying a cuent I in a unifom magnetic fiel as in figue Vetical suspene wie between magnet poles lat plane iew ( = q ) When thee is no cuent (I = 0) wie emains etical When I is upwa wie eflect to the left ( to the left) When I is ownwa wie eflect to the ight ( to the ight) Cuent caying wie will expeience if it exist in a -fiel. Insie the wie, a chages moe with along the length L will hae a magnetic foce, q o the total numbe of chages moing insie the wie = =, q ut ( q ) nv = ( q )nal I = qna = IL Whee n = /V o a staight wie in a unifom -fiel. L is a ecto of magnitue equal to length an iecte in the iection of cuent Chapte 8 Magnetic oce on a Cuent Caying Conucto If we consie an abitay shape wie of unifom coss sectional aea in an abitay - iel pat of total magnetic foce ( ) will occu fo the small segment length ecto (s ) = Is Total foce acting on the wie will be: b = I s a o an abitay wie in an abitay fiel. a an b ae en points of the wie a b Chapte 8 Magnetic oce on a Cuent Caying Conucto o abitay shape wie in unifom -fiel. b = I s = IL' a L is isplacement ecto between the en points) o a close loop wie in a unifom magnetic fiel stating point is same as en point ( s ) = 0 = I et magnetic foce acting on any close cuent loop in a unifom magnetic fiel is zeo. 5

Chapte 8 Magnetic oce on a Cuent Caying Conucto: emicicula conucto loop A semicicle wie in the xy plane of aius R foms a close cicuit an caies a cuent I.

6 Chapte 8 Magnetic oce on a Cuent Caying Conucto: emicicula conucto loop A semicicle wie in the xy plane of aius R foms a close cicuit an caies a cuent I. A unifom magnetic fiel is iecte along the positie y axis. in the magnitue an iection of the magnetic foce acting on the staight potion of the wie an on the cue potion. On the cue wie o = IL' = I s = = IL' = Isinθs = IR s = Rθ s = Rθ into the boa ( kˆ ) = IRsinθθ π The total foce on the = IRsinθθ close loop is 0 On the staight wie 1 = IL = = IR[ cosθ ] π = 1 = IL = IR = IR = IRkˆ IRkˆ Diecte out of the boa (kˆ ) into the boa ( kˆ ) = 0 Chapte 8: Toque on a Cuent Loop in a Unifom Magnetic iel eye Loop iew fom sie 3 Although the net -foce on a cuent loop must be zeo, we may hae a net toque ( دوران (عزم on it. Consie a ectangula cuent loop in a unifom -fiel, which is paallel to the plane of the loop o 1 an 3, L// L = 0 = 0 o an 4, L 4 = = Ia out of boa an 4 into boa net = 0. ut an 4 act on iffeent line of action they will pouce a toque τ (look at sie 3 to see othe iew) Cuent out of the boa Cuent into the boa Chapte 8: Toque on a Cuent Loop in a Unifom Magnetic iel If loop is fixe on piot (محور) O, Loop will otate clockwise a bout y-axis ue to the toque τ τ net = τ + τ 4 τ = with τ = sinθ At θ = 90 max. toque b b b b τ max = + 4 = ( Ia) + ( Ia) = ( Ia)b τ max = IA Whee A = ab is the aea of the loop If the -fiel makes an angle with a line pepenicula to the plane of the loop, then the toque is: b b b b τ = sinθ + 4 sinθ = Ia( + )sinθ τ = Iabsinθ = IAsinθ τ = IA Toque on cuent loop in unifom -fiel A is a ecto loop plane an its magnitue equal to A Concept Question A ectangula loop is place in a unifom magnetic fiel with the plane of the loop pepenicula to the iection of the fiel. If a cuent is mae to flow though the loop in the sense shown by the aows, the fiel exets on the loop: 3 4 A 1 1. a net foce.. a net toque. 3. a net foce an a net toque. 4. neithe a net foce no a net toque. (*) 6

iection of A The potential enegy of the loop is: U = µ Chapte 8: Toque on a Cuent Loop in a Unifom Magnetic iel: Magnetic ipole moment A ectangula coil of imensions 5.4 cm 8.

7 Chapte 8: Toque on a Cuent Loop in a Unifom Magnetic iel: Magnetic ipole moment = I A µ (Ampees.m ) is efine as magnetic ipole moment o (العزم المغناطيسي) often calle the magnetic moment τ = µ If the wie makes loops aoun A, τ = µ = µ loop µ has same iection as A coil with µ coil = IA In the iection of A The potential enegy of the loop is: U = µ Chapte 8: Toque on a Cuent Loop in a Unifom Magnetic iel: Magnetic ipole moment A ectangula coil of imensions 5.4 cm 8.5 cm consists of 5 tuns of wie an caies a cuent of 15 ma. A 0.35 T magnetic fiel is applie paallel to the plane of the coil. (A) Calculate the magnitue of the magnetic ipole moment of the coil. () What is the magnitue of the toque acting on the loop? A) ) τ = µ = µ θ = 90 loop coil ummay The ight han ule Magnetic foces on chage paticles an cuent caying wies Chage paticle motion in -fiel Toque on loops an magnetic ipole moments 7

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13