Magnetism Lecture Series. Electromagnetic Induction

Transcription

1 Magnetim Lecture Serie Electromagnetic Induction Applied Science Education Reearch Group (ASERG) aculty of Applied Science Unieriti Teknologi MARA Electric Charge Objectie/Learning outcome: 1. Decribe, explain and draw induced current in a coil when there i change in flux.. Decribe, explain and write mathematical relation to explain flux and flux change. 3. State araday Law and Len Law on electromagnetic induction and write related mathematical relation to determine induced electromotie force and induced current. 4. Dicu explain and derie mathematical relation to explain the mechanim of electric generator. Copyright DR JJ,SG, UiTM 1

2 Electric Charge Objectie/Learning outcome: 1. Decribe, explain and write mathematical relation for electric generator. Decribe, and explain about counter torque and back emf. 3. Decribe, explain and obtain mathematical relation about mutual, elf induction and energy tored in inductor. 4. Decribe, explain and obtain mathematical relation for tranformer. 5. Sole problem related to generator, inductor and tranformer. Copyright DR JJ,SG, UiTM 3 Magnetic ield Direction of the reultant force i determined by uing firt right hand rule : Point all finger in direction, thumb in direction, then palm will face direction of force q x q ( in θ ) Right-Hand-Rule 1: q egatie charge accelerate downward. to the right, out of page, then orce i upward. Hence the charge will accelerate upward. Copyright DR JJ,SG, UiTM 4

3 orce on wire Magnetic field produced by infinitely long wire Magnetic field denity or trength i proportional to the current through the wire and inerely proportional to the ditance from the wire. i, i/r Copyright DR JJ,SG, UiTM 5 Magnetic orce orce between wire loop Z Wire loop attract. Along center or z-axi, the field of each loop behae like a bar magnet with polaritie a hown. S S Copyright DR JJ,SG, UiTM 6 3

4 orce on wire orce on charge in Magnetic field produced by current-carrying infinitely long wire i 1 i πr Where i the permeability of free pace. 4π x 1-7 Tm/A q q i π r Copyright DR JJ,SG, UiTM 7 orce on wire i 3 r i 1 r i 1on3 1on3 1 1on3 1 3 i1 πr i3 πr i πr If L 1 L L 3, 1-1, on1 3on1 3on1 on on1 on1 3 on1 1on 1on 1on 1 il i1 il1 in θ i πr i1l1 i i1l1 in θ i 1 πr 1 1 on1 Copyright DR JJ,SG, UiTM 8 4

5 orce on wire orce on charge in Magnetic field produced by current-carrying infinitely long wire A currentcarrying infinitely long conductor placed near another currentcarrying infinitely long conductor will feel a magnetic force. i 1 r 1on i 1 1 i1 πr Copyright DR JJ,SG, UiTM 9 r D A What happen to the coil? orce on wire i 1 i1 π ( r w / ) A A x x x x x x x x D C x x x x C i1 C π ( r w / ) 1 ona i - D So, reultant horizontal force i zero. Since field along egment C i weaker, then Strength of A > trength of C. Then the coil will be attracted to the wire. Copyright DR JJ,SG, UiTM 1 L 1 il i1 π ( r w / ) il i1 1 onc il1 π ( r w / ) 5

6 Magnetic orce field at center of wire loop R S At the center of the loop, i i Z R R R i the radiu of the loop, i the number of turn A uual, point your thumb in the direction of the current, curl your finger, at the center of the loop that will how you direction of. Copyright DR JJ,SG, UiTM 11 Magnetic orce orce between infinitely long wire and a wire loop. In the diagram below, find the net field at the center of the loop of radiu R. r R R At the center of the loop, i i1 wire π r i loop R Out of plane Into the plane i 1 Total at center of loop i wire loop i1 i i1 ( i πr R R π ) Copyright DR JJ,SG, UiTM 1 6

7 Magnetic orce S orce between wire loop ield line of a ingle loop can be repreented like thoe of a bar magnet Copyright DR JJ,SG, UiTM 13 Magnetic orce orce between wire loop Z Wire loop attract. Along center or z-axi, the field of each loop behae like a bar magnet with polaritie a hown. S S Copyright DR JJ,SG, UiTM 14 7

8 Magnetic orce orce between wire loop Z Wire loop repel. Along center or z-axi, the field of each loop behae like a bar magnet with polaritie a hown. S S Copyright DR JJ,SG, UiTM 15 Magnetic orce field of a long olenoid When wire loop are wound cloe to each other, they form a olenoid. Along center or z-axi, the field of each loop behae like many bar magnet. The magnetic field denity, inide a long olenoid i ni, where n i number of turn per unit length, n /L. Copyright DR JJ,SG, UiTM 16 8

9 Magnetim Lecture Serie Electromagnetic Induction Induced Current/EM Current carrying wire induce magnetic field, o can arying field induce current in a circuit?? If field can be induced when current flow in a conductor, then urely the oppoite can happen The magnetic field line produced by a magnet far away and tationary from a coil will not induce any current in the coil. Copyright DR JJ,SG, UiTM 18 9

10 Induced Current/EM Current carrying wire induce magnetic field, o can arying field induce current in a circuit?? Current flowing mut be due to potential difference between end of the coil. Electromotie force EM mut exit between end of coil. When the magnet i moed cloer to the coil, more magnetic field line pae through the coil. The trength i alway increaing ince the number of line are increaing The needle of galanometer deflect to the right howing induced current in clockwie direction. Copyright DR JJ,SG, UiTM 19 Induced Current/EM Current carrying wire induce magnetic field, o can arying field induce current in a circuit?? The changing trength caue induced current. When the change top (no moement), the induced I diappear. When the magnet i moed away from the coil, le magnetic field line pae through the coil. The trength i alway decreaing ince the number of line are decreaing The needle of galanometer deflect to the left howing induced current in counter clockwie direction. Copyright DR JJ,SG, UiTM 1

11 Induced Current/EM Current carrying wire induce magnetic field, o can arying field induce current in a circuit?? When the area of the coil i changed, current i induced. The needle of galanometer deflect to the left and to the right alternately and continuouly a long a the area of the coil i continuouly increaed The changing trength or the and decreaed. change of coil area caue induced current. When the change top (no moement), the induced I diappear. Copyright DR JJ,SG, UiTM 1 Induced Current/EM Motional EM: EM induced in moing conductor. EM i induced wheneer there i a flux change through a coil, where flux i the number of field line through an area. Copyright DR JJ,SG, UiTM 11

12 Induced Current/EM t x x EM i induced wheneer there i a flux change through a coil. -- tt Where flux i the number of field line through an area. Charge top piling when E E q ε L q Motional EM: EM induced in moing conductor i: ε ε L xl t x x t t L Copyright DR JJ,SG, UiTM 3 x t L ε A t A A φ φ ε t t t t ( A) ε ( A co ϕ A ) ε A t φ Induced Current/EM E -- x x t tt Motional EM EM induced in moing conductor i: φ ε ( A) ε ( A co ϕ A ) ε EM i induced wheneer there i a flux change through a coil. Either the change, or the area change or imply if along the normal to the coil urface change. o EM induced if there i no change. lux i: φ A A co ϕ A Product of area and component of parallel to normal of A. Copyright DR JJ,SG, UiTM 4 1

13 Induced Current/EM lux ε A A co ϕ A lux i the total number of line which pae through the urface of a coil. Meaured in unit of weber or Wb. lux i maximum when and the normal of the coil urface i parallel, minimum when oppoite direction and zero when no line pa through urface (9 degree) Copyright DR JJ,SG, UiTM 5 Induced Current/EM lux A ϕ ϕ par per φ A ( co ϕ A ) A per par ϕ ϕ A Copyright DR JJ,SG, UiTM 6 13

14 Induced Current/EM ind I -- araday Law of Electromagnetic Induction: The induced EM i proportional to the time rate of change of the flux. φ ε ( A co ϕ ε The induced EM caue induced current to flow and when there i induced current flowing, thi caue an induced magnetic force a hown aboe which will tend to oppoe to change motion of the rod to the right. A ) Copyright DR JJ,SG, UiTM 7 Induced Current/EM araday Law: The induced EM i proportional to the time rate of change of the flux. A parallel to A. lux maximum A perpendicular to A. lux zero φ final φ ε φ max ε A φ max initial A parallel to A. lux maximum ϕ A lux i Aco ϕ A co ϕ ε A Copyright DR JJ,SG, UiTM 8 A A( 1 co ϕ ε A ) 14

15 Induced Current/EM I -- How to determine polarity of induced EM?? Lenz Law of Electromagnetic Induction φ ε EM induced due to changing flux ha polarity that lead to induced current which will induce a field that will counter or oppoe the original flux change. Copyright DR JJ,SG, UiTM 9 Induced Current/EM S Lenz Law of Electromagnetic Induction φ ε EM induced due to changing flux ha polarity that lead to induced current which will induce a field that will counter or oppoe the original flux change. Induced I mut be CCW o that it can produce with orth pole to the left of coil. Copyright DR JJ,SG, UiTM 3 15

16 Induced Current/EM Lenz Law of Electromagnetic Induction 1. I flux increaing or decreaing?. What i the direction of the induced flux o a to oppoe flux change? 3. Ue RHR- to find direction of induced current and then aign polarity. Picture 1:lux increaing. Induced I mut be CCW o that it can produce with orth pole out of paper Picture : o flux change Picture 3:lux decreaing. Induced I mut be CCW o that it can produce with orth pole into of paper Copyright DR JJ,SG, UiTM 31 Induced Current/EM Generator : Rotate coil in a magnetic field and produce current EM i induced wheneer there i a flux change through a coil. A generator produce current when the coil i rotated by external agent, in a magnetic field. Copyright DR JJ,SG, UiTM 3 16

17 Induced Current/EM Generator : Rotate coil in a uniform magnetic field and produce current. ront iew. Clockwie rotation w ϑ x L 1 3 Axi of rotation Uing RHR-1, determine charge accumulation on the armature and the direction of induced emf and hence induced current (clockwie) Copyright DR JJ,SG, UiTM 33 Induced Current/EM Generator : Rotate coil in a uniform magnetic field and produce current. ront iew. Clockwie rotation w ϑ x L 1 3 Axi of rotation q ε ε ql L Arm 1 only oth arm 1 & 3 ε L in θ ε L in θ Copyright DR JJ,SG, UiTM 34 17

18 Induced Current/EM Generator : Mechanically rotate coil in a uniform magnetic field and produce current. ront iew. Clockwie rotation w ϑ x L 1 3 Axi of rotation or 1 ide only ε L in θ ε ide ε L in θ rω ε Lr ω in θ ε L ( w / ) ω in θ Aω in θ ε ε in θ Copyright DR JJ,SG, UiTM 35 Induced Current/EM Generator : Rotate coil in a magnetic field and produce alternating current The angle between the linear elocity and the magnetic field i related to it angular frequency and o the the EM produced can be repreented a a function of time a hown in picture. ε ε in θ ε ε in ωt θ θ θ ω t t t EM produced i a inuoidally changing from ε to - ε and paing through zero. Copyright DR JJ,SG, UiTM 36 18

19 Induced Current/EM Mutual Induction : A coil placed near another coil with alternating current paing thru it, will hae current induced in it. Inductor tore & produce field Alternating current I p in primary coil induce fluctuating current in econd coil to counter the change cauing it to change (araday & Lenz Law. ε ε in ωt Φ ε φ lux change thru econdary i proportional to change in primary current. φ I p φ MI p Copyright DR JJ,SG, UiTM 37 Induced Current/EM Mutual Induction : A coil placed near another coil with alternating current paing thru it, will hae current induced in it. Inductor tore & produce field Define mutual inductance a M φ I p Where φ flux thru 1 loop and i the number of turn. Since induced flux in a coil i ( φ ) ε ( MI p ) Hence emf induced i I ε M p Copyright DR JJ,SG, UiTM 38 19

20 Induced Current/EM Mutual Induction : A coil placed near another coil with alternating current paing thru it, will hae current induced in it. Inductor tore & produce field Since induced flux in a coil i ( φ ) ε ( MI p ) Define mutual inductance a M φ I I ε M p I ε M p p Hence emf induced i At the ame time, emf induced in primary coil i Copyright DR JJ,SG, UiTM 39 Induced Current/EM Self Induction : The changing field created by the eer changing current in a coil change flux in the coil and hence induce emf in that coil. Hence emf induced in coil i ( LI ) I ε L φ ( φ ) ε ut flux change i due to I changing in the coil. φ I Where L i elf-inductance L & M range from micro to millihenry. Inductor tore magnetic energy of trength Then, φ Copyright DR JJ,SG, UiTM 4 LI LI Energy

21 Induced Current/EM Self Induction : The changing field created by the eer changing current in a coil change flux in the coil and hence induce emf in that coil Since energy tored in inductor i LI Then E φ LI LI φ and energy E I i I A nia E I I I or olenoid, about center i ni where n /L, then energy tored in a olenoid i Then E Energy denity or energy per unit olume nial n I I AL L L E n I AL L L Copyright DR JJ,SG, UiTM 41 1