Magnetic flux

NCEA Level 3 Physics Electricity AS91526 Magnetic Flux

1. Magnetic Flux

2. Magnetic Flux Magnetic Flux ( symbol  B ) is a measure of the magnetic field strength present over a given area. The units are Weber (symbol Wb )  B = BA Last year we looked at B magnetic field strength which is Φ B /A ( that’s why B is also called flux density) This year we are interested in;

3. Examples A magnetic field of a small NIB* magnet is 0.2T and covers an area of 0.12m 2 . Calculate the magnetic flux. 0.024Wb A magnetic flux of 2.5Wb is measured in an area of 0.25m 2 . Calculate the flux density (magnetic field strength). 10T A strong electromagnet produces a field with a flux density of 1.5T and has a flux of 0.54Wb. Calculate the area that the field covered. 0.36m 2 *NIB short for the alloy of neodymium, iron, and boron

4. Faraday’s Law of Induction Any change in a magnetic field will induce a voltage and thereby a current in a circuit. The faster this change occurs, the larger the induced voltage (a voltage can be induced by a magnet moving in and out of a coil or past a conductor, a wire moving through a magnetic field, or by the growth or collapse of a magnetic field)

5. Faraday’s Law of Induction An emf (voltage) is induced in a circuit only if Φ B changes within the circuit, i.e. if the magnitude of B changes. if the direction of B changes If the position of B changes if the area enclosed by the circuit changes where; ε = emf or voltage (V) Δ Φ =change in flux ( Wb ) Δt = change in time (s)

6. Changing the Magnetic Flux in a Constant Magnetic Field

7. Examples Find the induced emf when a change in flux of 0.56Tm 2 occurs in 0.02s. 28V A magnetic field of 0.20T forms across and area of 0.12m 2 in 0.02s. Calculate the emf induced 1.2V A very strong electromagnet creates a magnetic field of 1.5T at a frequency of 25Hz over an area of 25cm 2 . Calculate the emf induced in a wire within the field. 0.94V

8. Lenz’s Law An induced current is always in such a direction as to oppose the motion or change causing it This helps explain the negative sign in Faraday’s Law;

9. Direction of Induced Current induced I opposes the motion of magnet (being attracted ) induced I opposes the motion of magnet (being repelled )

10. Direction of Induced Current In both cases, magnet moves against a force . Work is done during the motion & it is transferred as electrical energy.

11. Try these; A bar magnet passes through a coil: Indicate the direction of the induced I in each case. Explain briefly. ( i) ( ii) ( iii)

12. Answer ( i) Indicate the direction of the induced I . Explain. ( i) When magnet’s N-pole is moving into coil, induced I flows in such a direction as to produce a N-pole to oppose the approaching of magnet. Lenz’s law I S N

13. Answer ( ii ) Indicate the direction of the induced I . Explain. ( ii) The induced I become zero  I is about to change direction .

14. Answer ( iii ) Indicate the direction of the induced I . Explain. ( iii) When magnet’s S-pole is leaving the coil, induced I flows in such a direction as to produce a N-pole to oppose the leaving of magnet. I N S

15. Lenz’s Law Use the RH Grip rule for Solenoids and Lenz’s law to predict the magnetic poles formed by the coils below

16. Lenz’s Law Predict the poles and the current direction for each of the following;

17. Lenz’s Law and Energy Lenz’s law makes sense if we think about the conservation of energy. The electrical energy induced must come from work being done. e.g. a greater force (W= Fd ) must be applied to move the magnet through a solenoid, than through open space, as some of the mechanical energy is being converted into electrical energy.

18. Lenz’s Law –the Maths The induced emf produces a current that opposes the change that produces it (i.e. the emf tries to keep the flux constant or to compensate for the change in flux). Lenz’s law determines the direction of current flow and accounts for the negative sign in Faraday’s Law. For a circuit consisting of N wire loops (e.g. a coil): Faraday’s Law of Induction for a single circuit loop:

19. Induced Voltage (emf) An emf is induced in a conductor moving in a magnetic field. A conducting wire of length L moves perpendicularly to a uniform magnetic field B with constant velocity v . Force on electrons in the wire: Since force F on electrons is upward, I is downward in the wire. An emf is induced and a current flows in the wire as long as it moves in the magnetic field. (principle of the electric generator). (Potential difference)

20. Example A single rectangular loop of wire (0.230 Ω) sits in a region of uniform magnetic field of 0.450 T . Calculate the voltage induced in the loop as it is pulled out of the field (to the right) at a constant velocity of 3.40 m/s. What is the magnitude and direction of the current flowing in the loop during this motion?

21. Working V=BvL =0.450×3.4×0.350 =0.5355 V =0.536V (3sf) I=V/R =0.5335/0.230 =2.328A =2.33A (3sf) anticlockwise

22. Example -rethink This too is a Faraday’s law problem;  =BA =0.450×0.350× 0.350 =0.05512 Time taken to move through the field (B from 0.450T to 0T) t=d/v = 0.350 /3.4 =0.1029 s Faraday’s Law V= Δ / Δ t =0.05512/0.1029 =0.5355V Use any breadth for area as long as use same for distance travelled

23. Examples The Airbus A380 has a wingspan of 78.6m. Calculate the induced voltage across the wingtips when it flies through the earth’s magnetic field (5×10 -5 T) (vertically down) at 900kmh -1 0.98V A coil connected to a voltmeter is moved through a magnetic field of 0.2T at 2.4ms -1 . Find the length of the coil if the induced voltage is 1.5V. 3.1m Why is it not possible to use the voltage in Question 1?

24. Uses of Induction The Electric Generator using mechanical energy to turn a motor and produce electrical energy. The Transformer uses one coil to induce a current in another The Inductor an electrical component that produces and induced current and behaves like a very efficient resistor in an AC circuit

25. The Transformer An electrical transformer is an arrangement of two coils usually around a laminated iron core The primary coil induces a voltage and therefore a current in the secondary coil The ratio of the number of turns on each coil determines the output voltage of the secondary coil Symbol;

26. Iron Core The efficiency of a transformer is greatly increased by placing an iron core between the primary and secondary coils. The core greatly increases the magnetic field. Cores are laminated to reduce inductance within the core itself, which can cause eddy currents that result in energy loss through heating (resistance). Each laminate is insulated from it’s neighbour The use of non-conducting, magnetic material such as ferrite as a core also avoids eddy currents

27. Laminated Iron Core

28. Types of Transformers There are three basic types of transformer; Step up Transformer low voltage and higher output voltage Isolating Transformer Used to produce an “isolated” circuit that is safe for using electrical appliances outdoors Step down Transformer High input voltage and lower output voltage

29. DC in Transformers According to Faraday’s Law ; voltage is induced only when the flux changes In a DC circuit that is only when the current is switched on (field created) or off (field collapsed)

30. AC in Transformers Transformers are most commonly used in AC circuits because the constantly changing direction of the current means that induction is continuous

31. Transformers in Action

32. Transformers -Mathematically In the ideal transformer; and Transformer efficiency is never 100% as there are always “loses” of energy e.g heat, sound? etc. However good design has given some 99% efficiency

33. Examples A primary coil of a transformer has primary voltage of 12V and 36 turns. How many turns will be needed on the secondary coil to give an output voltage of 20V? 48 turns The output voltage of a transformer is 15V. Find the input voltage if N P =600 and N s =75. 120V

34. Examples (con’t) A step up transformer has 12V across the primary (1 ) coil which carries a current of 1.4A. Calculate the voltage of the 2  coil if the current is 0.15A 112V An isolating transformer has 240V across its 1  coil and 10A. What is the efficiency of the transformer if the 2  coil produces 240V with a current of 8.5A? 85%

35. Exercises Pg 247 Activity 15B

36. Inductance Inductance is the ability of an inductor to store energy in a magnetic field

37. Mutual Inductance Transformers use the changing current in the primary coil to induce a voltage in the secondary coil this is Mutual Inductance . The current in coil A can be changed by; changing the resistance of the variable resistor switching the circuit on and off connecting it to an AC supply

38. Mutual Inductance –the Maths When mutual inductance occurs the flux is proportional to the current in the primary coil Substituted into Faraday’s law; Units for mutual inductance is the Henry (symbol H) Where;  =magnetic flux (Wb) M=mutual inductance (H) I= Current(a)

39. E xercises Two coils have a mutual inductance of 0.060H. Calculate the induced emf when the current in the 1  increases from 0 to 4.5A in 1.5s 0.18V Find the mutual inductance between two coils when the current in the 1  increases from 0 to 2.8A in 0.5s and the induced voltage is 80mV. 0.014H

40. Self Inductance When a switch is closed and current flows through a coil it will take time (usually a very short time) for the current to build up from 0 to a steady flow. As the current is increasing the magnetic flux in the coil is changing This change in flux induces a voltage and therefore a current in the coil This induced current is in such a direction so as to oppose the current that created it This is self-inductance When the switch is closed the same thing happens with the induced current in the opposite direction

41. Self Inductance in AC When an inductor is attached to an AC supply the inductor behaves like a resistor restricting the flow of current The inductor is an efficient way to restrict current as it uses induction rather than resistance The inductor stores electrical energy in a magnetic field then releases it as electrical energy. The resistor converts some electrical energy to heat which is then “lost” from the circuit

42. Self-inductance and Circuit Voltage A Neon bulb takes about 70V to ionise the gas and light the bulb Closing the switch causes current to flow and the inductor produces a small induced voltage briefly as the flux changes. Opening the switch however causes the lamp to light briefly Because of the high resistance of the lamp, the collapse of the field is very rapid o the induced voltage is large (>70V)

43. Inductors Inductors are electrical components that make use of the principal described by Lenz’s law. They produce a magnetic field when current passes through them. This field induces a voltage and therefore a current that opposes the current that created it. An Inductor is an electrical component that produces a voltage when the current (and therefore the magnetic field) changes

44. Inductor Structure The wire coil of the inductor is usually wound around an iron core to increase the field strength Because the inductor is a length of wire it has a resistance so inductors are often drawn with a resistor in a similar way to the internal resistance of a battery An ideal inductor has a resistance small enough to be ignored

45. Self Inductance –the Maths When self inductance occurs the flux is proportional to the current in the inductor Substituted into Faraday’s law; Units for self-inductance is the Henry (symbol H) Where;  =magnetic flux ( Wb ) L=self-inductance (H) I= Current(a)

46. E xercises An ideal inductor has a inductance of 0.060H. Calculate the induced emf when the current increases from 0 to 2.8A in 1.2s 0.14V Find the terminal voltage of an inductor with an inductance of 0.040H and a resistance of 0.60 when the current increases from 0 to 2.5A in 0.4s. -1.25

47. Energy stored in an Inductor Current in an inductor causes a magnetic field to form. Energy is stored in this field. An inductor in a circuit with a bulb can delay the lighting of the bulb as the electrical energy is stored in the magnetic field

48. E xercises An ideal inductor has a inductance of 0.080H. Calculate the energy stored in the inductor when the current is 4.5A. 0.81J Find inductance of an inductor that stores 1.8J of energy when the current is 3.8A. 0.25H

49. Exercises Read Pg 249-253 Do Activity 15C

50. Voltage and Current Graphs for Inductors

51. Voltage and Current of Inductors When a switch is closed it takes time for the current to reach a steady flow The change in current through the inductor induces an emf The induced current opposes the current that created it (slowing down the rate of change –slope of graph) The greatest induced voltage is when Δ I is greatest ( Faraday’s law) As Δ I decreases so does V L Time Voltage Current Time The shape of these curves can be controlled by a resistor in series, the higher the resistance the slower the rate of change

52. Voltage and Current of Inductors When a switch is opened it takes time for the current to decrease to 0 The change in current through the inductor induces an emf The induced current opposes the current that created it (slowing down the rate of change –slope of graph) The greatest induced voltage is when Δ I is greatest ( Faraday’s law) As Δ I decreases so does V L Time Voltage The shape of these curves can be controlled by a resistor in series, the higher the resistance the slower the rate of change Time Current

53. Voltage and Current of Inductors Being able to describe the changes in V and I of inductors is important Consider the switch positions in the circuit and the graphs

54. Time Constant ( ) One time constant is the time taken for I L or V L to change by 63% i.e. the time for current to reach 63% of I L (or 36.5% when switched off) or for V L to reach 37% Experts; this is because of the exponential nature of the curves; I L t 63.5% V L t 37.5%

55. Time Constant ( ) -the maths The shape of the I/t and V/t curves is controlled by a resistance (R) of the circuit and the self-inductance (L) of the inductor Remember that R will include the resistance of the inductor as well as any other resistance in the circuit

56. Examples A circuit with a resistance of 28  has a 0.75 H inductor in it. Calculate the Time constant of the inductor. Find the resistance of a circuit where a 0.50H inductor has a time constant of 1.8s