Electromagnetic Induction

1. Electromagnetic Induction • emf is induced in a conductor placed in a magnetic field whenever there is a change in magnetic field.

2. Moving Conductor in a Magnetic Field • Consider a straight conductor moving with a uniform velocity, v, in a stationary magnetic field. • The free charges in the conductor experience a force which will push them to one end of the conductor. • An electric field is built up due to the electron accumulation. • An e.m.f. is generated across the conductor such that E = Blv.

3. Induced Current in Wire Loop • An induced current passes around the circuit when the rod is moved along the rail. • The induced current in the rod causes a force F = IlB, which opposes the motion. • Work done by the applied force to keep the rod moving is • Electrical energy is produced from the work done such that E = E It = W E= Blv

4. Lenz’s Law • The direction of the induced current is always so as to oppose the change which causes the current.

5.  Magnetic Flux • The magnetic flux is a measure of the number of magnetic field lines linking a surface of cross-sectional area A. • The magnetic flux through a small surface is the product of the magnetic flux density normal to the surface and the area of the surface. Unit : weber (Wb)

6. Faraday’s Law of Electromagnetic Induction • The induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage through the circuit. The ‘-’ sign indicates that the induced e.m.f. acts to oppose the change. http://physicsstudio.indstate.edu/java/physlets/java/indcur/index.html

7. Induced Currents Caused by Changes in Magnetic Flux • The magnetic flux (number of field lines passing through the coil) changes as the magnet moves towards or away from the coil. http://micro.magnet.fsu.edu/electromag/java/lenzlaw/index.html

8. Faraday Disk Dynamo

9. Simple a.c. Generator • According to the Faraday’s law of electromagnetic induction, http://www.walter-fendt.de/ph11e/generator_e.htm

10. Simple d.c. Generator

11. Eddy Current • An eddy current is a swirling current set up in a conductor in response to a changing magnetic field. • Production of eddy currents in a rotating wheel

12. Applications of Eddy Current (1) • Metal Detector

13. Applications of Eddy Current (2) • Eddy current levitator • Smooth braking device • Damping of a vibrating system

14. Back emf in Motors • When an electric motor is running, its armature windings are cutting through the magnetic field of the stator. Thus the motor is acting also as a generator. • According to Lenz's Law, the induced voltage in the armature will oppose the applied voltage in the stator. • This induced voltage is called back emf.

15. Armature coils, R Back emf, Eb Driving source, V Back emf and Power • So the mechanical power developed in motor MultiplyingbyI, then

16. I t 0 Variation of current as a motor is started • As the coil rotates, the angular speed as well as the back emf increases and the current decreases until the motor reaches a steady state. Larger load Zero load

17. The need for a starting resistance in a motor • When the motor is first switched on,  =0. • The initial current, Io=V/R, very large if R is small. • When the motor is running, the back emf increases, so the current decrease to its working value. • To prevent the armature burning out under a high starting current, it is placed in series with a rheostat, whose resistance is decreases as the motor gathers speed.

18. I  0 Variation of current with the steady angular speed of the coil in a motor • The maximum speed of the motor occurs when the current in the motor is zero.

19. Po  0 Variation of output power with the steady angular speed of the coil in a motor • The output power is maximum when the back emf is ½ V.

20. Transformer • A transformer is a device for stepping up or down an alternating voltage. • For an ideal transformer, • (i.e. zero resistance and no flux leakage)

21. Transformer Energy Losses • Heat Losses • Copper losses- Heating effect occurs in the copper coils by the current in them. • Eddy current losses- Induced eddy currents flow in the soft iron core due to the flux changes in the metal. • Magnetic Losses • Hysteresis losses- The core dissipates energy on repeated magnetization. • Flux leakage- Some magnetic flux does not pass through the iron core.

22. Designing a transformer to reduce power losses • Thick copper wire of low resistance is used to reduce the heating effect (I2R). • The iron core is laminated, the high resistance between the laminations reduces the eddy currents as well as the heat produced. • The core is made of very soft iron, which is very easily magnetized and demagnetized. • The core is designed for maximum linkage, common method is to wind the secondary coil on the top of the primary coil and the iron core must always form a closed loop of iron.

23. Transmission of Electrical Energy • Wires must have a low resistance to reduce power loss. • Electrical power must be transmitted at low currents to reduce power loss. • To carry the same power at low current we must use a high voltage. • To step up to a high voltage at the beginning of a transmission line and to step down to a low voltage again at the end we need transformers.

24. Direct Current Transmission • Advantages • a.c. produces alternating magnetic field which induces current in nearby wires and so reduce transmitted power; this is absent in d.c. • It is possible to transmit d.c. at a higher average voltage than a.c. since for d.c., the rms value equals the peak; and breakdown of insulation or of air is determined by the peak voltage. • Disadvantage • Changing voltage with d.c. is more difficult and expensive.

25. Self Induction • When a changing current passes through a coil or solenoid, a changing magnetic flux is produced inside the coil, and this in turn induces an emf. • This emf opposes the change in flux and is called self-induced emf. • The self-induced emf will be against the current if it is increasing. • This phenomenon is called self-induction.

26. Definitions of Self-inductance (1) • Definition used to find L The magnetic flux linkage in a coil  the current flowing through the coil. Where L is the constant of proportionality for the coil. L is numerically equal to the flux linkage of a circuit when unit current flows through it. Unit : Wb A-1 or H (henry)

27. Definitions of Self-inductance (2) • Definition that describes the behaviour of an inductor in a circuit Lis numerically equal to the emf induced in the circuit when the current changes at the rate of 1 A in each second.

28. Inductors • Coils designed to produce large self-induced emfs are called inductors (or chokes). • In d.c. circuit, they are used to slow the growth of current. • Circuit symbol or

29. Inductance of a Solenoid • Since the magnetic flux density due to a solenoid is • By the Faraday’s law of electromagnetic induction,

30. Energy Stored in an Inductor • The work done against the back emf in bringing the current from zero to a steady value Io is

31. Current growth in an RL circuit • At t = 0, the current is zero. • So • As the current grows, the p.d. across the resistor increases. So the self-induced emf ( - IR) falls; hence the rate of growth of current falls. • As t

32. Decay of Current through an Inductor • Time constant for RL circuit • The time constant is the time for current to decrease to 1/e of its original value. • The time constant is a measure of how quickly the current grows or decays.

33. - + emf across contacts at break • To prevent sparking at the contacts of a switch in an inductive circuit, a capacitor is often connected across the switch. The energy originally stored in the magnetic field of the coil is now stored in the electric field of the capacitor.

34. - + Switch Design • An example of using a protection diode with a relay coil. • A blocking diode parallel to the inductive coil is used to reduce the high back emf present across the contacts when the switch opens.

35. Non-Inductive Coil • To minimize the self-inductance, the coils of resistance boxes are wound so as to set up extremely small magnetic fields. • The wire is double-back on itself. Each part of the coil is then travelled by the same current in opposite directions and so the resultant magnetic field is negligible.