1. Topic 9.33.2.1 Electromagnetic Induction

2. Inducing an EMF In the 1830s when Michael Faraday moved awire through a magnetic field just to see whathappened, he discovered that a small pulse ofcurrent was generated. He hypothesised that the magnetic field createda force on the electrons causing them to movealong the wire. He dubbed this force an electromotive force i.e. a force that causes the movement of electrons. This often abbreviated as emf 3. Inducing an EMF He knew that electrons could flow (a current)only if there was a potential difference (avoltage) present. He reasoned that the emf caused an imbalanceof charge i.e. one end of the rod was more negative than theother. Hence an induced voltage along the length ofthe wire. 4. Inducing an EMF He found that an emf was only created whenthe wire was moved. If it was held stationary then no emf was created. When the wire was moved in the oppositedirection, the emf was generated in theopposite direction. If he used stronger magnets a larger emf wasgenerated. emf is dependent on magnetic field 5. Inducing an EMF If he moved the wire faster a larger emf wasgenerated. emf is dependent on velocity If he moved a coil of wire a larger emf wasgenerated. emf is dependent on the number of coils. If he moved the magnet instead of the wire therewas no change in the results. Emf is dependent on relative motion between thewire and magnetic field. 6. Induced EMF The direction of theinduced current is givenby Flemmings righthand rule. First finger = Field seCond finger = Current Thumb = Thrust (force & motion) NOTE this is the opposite of the motor(gun) rule. 7. Deriving induced EMF(Beyond HSC Syllabus) Consider a wire moving in amagnetic field The electrons in the wire willexperience a force on them as thewire moves. The electrons will move along thewire creating an imbalance andhence an electric field. When the E field and the B-field areequal the electrons stop moving.+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + +I+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + B +vFB=BIl=B(Qt)l=BQ( lt )=BqvFE=qEFB=FEq Bv=q EBv=E 8. Deriving induced EMF(Beyond HSC Syllabus) When the E field and theB-field are equal theelectrons stop moving. This also shows that anelectric field is created bya moving (changing)magnetic field.+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + +I+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + B +vFB=FEq Bv=q EBv=E 9. Deriving induced EMF(Beyond HSC Syllabus) If the electric field along thewire is considered to beuniform then. Where is the induced emf. Therefore by substitution thisbecomes. Or if the wire is a coil on nturns.+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + +I+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + B +vE=Vl=l=l Bv=n l Bv 10. Induced EMF Faraday was working with large coils of wire andfound that this simple derivation did not work perfectly. He found that coils with bigger areas induced biggeremfs. He reasoned that because the EMF was dependenton both the magnetic field strength and the area aswell as the velocity, the emf was really dependent onthe rate of cutting of magnetic flux lines. This is known as Faradays law. 11. Magnetic Field and Flux A magnetic flux line is an imaginary line which determines thedirection in which a north monopole magnet (if one could exist)would move if placed in a field. As already defined, the magnetic field strength B is the density ofthe magnetic flux lines. The total magnetic flux penetrating an area (a surface) near amagnetic field source is given by:=B A Magnetic flux is a scalar quantity while flux density is a vector. Magnetic flux is measured in Tesla-square-metres (Tm2) orWebers (Wb) 12. Faradays Law As the wire moves upthrough the field it sweepsout an area per second ofAt=ldt But because the speed ofthe wire is v, this becomesAt=l (v) Therefore the inducedemf is.=n Bl v=n B At+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + +I+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + B +vIv 13. Faradays Law The magnetic flux densitymultiplied by area givesthe total magnetic flux.=BA Therefore the inducedemf is given by:=n t+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + +I+ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + B +vIv 14. Lenzs Law Heinrich Lenz observed that the direction of aninduced emf always acts to provide a resistiveforce and not an accelerating force. This is also required when considering the lawof conservation of energy. Lenz's law states that The induced emf is such that the induced currentcreates a magnetic field that opposes the thechange producing it. 15. Faraday's Law Faraday's law when combined with Lenz's lawgives us the induction formula:=n t Note the negative sign which indicates thereversed direction of the induced emf. 16. Motors and emf A motor works on the principle of a current in acoil of wire placed in a magnetic fieldgenerating a torque. However, when a coil is turned in a magneticfield it also generates an emf. Which rule is true for a motor? Both! The turning motor produces a back emfwhich tries to resist the turning torque. 17. Back emf in Motors A motor can be(simply) modelled as aresistor. Technically thereshould also be aninductor but this is notrelevant if we assumeslow speeds.MotorRVs 18. Back emf in Motors When the motor isturned on it acts as ifthere is an additionalbattery inside themotor. This is the back emf. Notice that the backemf opposes thesupply emf.MotorRVsVback 19. Back emf in Motors The back emf causesthe motor current tofall when the motor isspinning. Using Ohm's law:MotorRVsVbackI=VR 20. Back emf in Motors When the motor starts, theback emf is zero (as the coilis not turning) so the currentis:I Vback max= When the motor is running ata steady speed, the back emfis not zero so the current is:MotorRVsV sRI run=V sV backRTimeCurrent 21. Eddy Currents When a conductor is near achanging magnetic field, Lenz's lawstates that an emf will be induced that Induces a current that Induces a magnetic field that Opposes the changing field. These small circular currents in theconductor are known as Eddycurrents 22. Eddy Currents If the conductor swingsthrough a fixed magneticfield, Eddy currents areproduced which produce a magneticbraking force and the pendulum stopsswinging 23. Eddy Currents If the conductor has slots init then: the eddy currents aresmaller and they produce A smaller magnetic fieldwhich produces a smaller magnetic brakingforce and the pendulum stopsswinging more slowly. 24. Electromagnetic Braking Eddy currents are commonly used as afail safe braking system on rollercoasters. Magnets are placed at the side of thetrack and large metal plates are placedon the bottom of the cars to passbetween them. Eddy currents are formed in the brakes A force is induced The roller coaster comes to a gentlestop. The faster the coaster is going thebigger the current and the higher thestopping force. 25. Electromagnetic Braking Electromagnets could also be used toprovide the external field. This allows electromagnetic braking tobe used on large vehicles such astrains and on high performancevehicles like racing cars. Being non contact brakes they tend tolast longer than friction brakes as wellas being smoother acting.