PHYSICS PROJECT REPORT MUTUAL INDUCTION

INDEX

1.ACKNOWLEDGEMENT

2.CERTIFICATE

3.AIM

4.INTRODUCTION

5.HISTORY

6.APPLICATIONS

7. ELECTRICAL GENERATOR

8. ELECTRICAL TRANSFORMER

9. EDDY CURRENTS

10. ELECTROMAGNET LAMINATIONS

11. PARASTIC INDUCTION WITH INDUCTORS

12. BIBLIOGRAPHY

AIM

To make a

PHYSICS PROJECT REPORT ON 

MUTUAL INDUCTION

ACKNOWLEDGEMENT

It is my duty to record my sincere thanks and deep sense of gratitude to my respected teachers

for their valuable guidance, interest and constant encouragement for the fulfilment of the project.

I am also highly obliged to our lab teacher who provided me the required apparatus and materials.

---

CERTIFICATE

This is to certify that

………………………………

has worked under my supervision on

The Project

PHYSICS PROJECT REPORT ON

MUTUAL INDUCTION

and  completed it to my satisfaction.

                                                                        Teacher’s

__________________________________________

__________________________________________

__________________________________________

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Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday’s law of induction. Lenz’s law describes the direction of the induced field. Faraday’s law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell’s equations in James Clerk Maxwell’s theory of electromagnetism.

Electromagnetic induction has found many applications in technology, including electrical components such as inductors and transformers, and devices such as electric motors and generators.

Part of a series of articles about
Electromagnetism
Electricity Magnetism
Electrostatics[show]
Magnetostatics[show]
Electrodynamics[hide] Lorentz force law Electromagnetic induction Faraday’s law Lenz’s law Displacement current Magnetic potential Maxwell’s equations Electromagnetic field Electromagnetic pulse Electromagnetic radiation Maxwell tensor Poynting vector Liénard–Wiechert potential Jefimenko’s equations Eddy current London equations Mathematical descriptions of the electromagnetic field
Electrical network[show]
Covariant formulation[show]
Scientists[show]
v t e

History[edit]

Electromagnetic induction was first discovered by Michael Faraday, who made his discovery public in 1831.^[3][4] It was discovered independently by Joseph Henry in 1832.^[5][6]

In Faraday’s first experimental demonstration (August 29, 1831), he wrapped two wires around opposite sides of an iron ring or “torus” (an arrangement similar to a modern toroidal transformer).^{[citation needed]} Based on his understanding of electromagnets, he expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. He saw a transient current, which he called a “wave of electricity”, when he connected the wire to the battery and another when he disconnected it.^[7] This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected.^[2] Within two months, Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead (“Faraday’s disk”).^[8]

Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically.^[9] An exception was James Clerk Maxwell, who used Faraday’s ideas as the basis of his quantitative electromagnetic theory.^[9][10][11] In Maxwell’s model, the time varying aspect of electromagnetic induction is expressed as a differential equation, which Oliver Heaviside referred to as Faraday’s law even though it is slightly different from Faraday’s original formulation and does not describe motional EMF. Heaviside’s version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell’s equations.

In 1834 Heinrich Lenz formulated the law named after him to describe the “flux through the circuit”. Lenz’s law gives the direction of the induced EMF and current resulting from electromagnetic induction.

Theory[edit]

Faraday’s law of induction and Lenz’s law[edit]

Faraday’s law of induction makes use of the magnetic flux Φ_B through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral:^[12]

{\displaystyle \Phi _{\mathrm {B} }=\int \limits _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \ ,}

where dA is an element of the surface Σ enclosed by the wire loop, B is the magnetic field. The dot product B·dA corresponds to an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.

When the flux through the surface changes, Faraday’s law of induction says that the wire loop acquires an electromotive force(EMF).^{[note 1]} The most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit:^[16][17]

{\displaystyle {\mathcal {E}}=-{{d\Phi _{\mathrm {B} }} \over dt}\ },

where {\displaystyle {\mathcal {E}}} is the EMF and Φ_B is the magnetic flux. The direction of the electromotive force is given by Lenz’s law which states that an induced current will flow in the direction that will oppose the change which produced it.^[18] This is due to the negative sign in the previous equation. To increase the generated EMF, a common approach is to exploit flux linkage by creating a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them. The resulting EMF is then Ntimes that of one single wire.^[19][20]

{\displaystyle {\mathcal {E}}=-N{{d\Phi _{\mathrm {B} }} \over dt}}

Generating an EMF through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways:

1. the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger),
2. the wire loop is deformed and the surface Σ changes,
3. the orientation of the surface dA changes (e.g. spinning a wire loop into a fixed magnetic field),
4. any combination of the above

Maxwell–Faraday equation[edit]

In general, the relation between the EMF {\displaystyle {\mathcal {E}}} in a wire loop encircling a surface Σ, and the electric field E in the wire is given by

{\displaystyle {\mathcal {E}}=\oint _{\partial \Sigma }\mathbf {E} \cdot d{\boldsymbol {\ell }}}

where dℓ is an element of contour of the surface Σ, combining this with the definition of flux

{\displaystyle \Phi _{\mathrm {B} }=\int \limits _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \ ,}

we can write the integral form of the Maxwell–Faraday equation

{\displaystyle \oint _{\partial \Sigma }\mathbf {E} \cdot d{\boldsymbol {\ell }}=-{\frac {d}{dt}}{\int _{\Sigma }\mathbf {B} \cdot d\mathbf {A} }}

It is one of the four Maxwell’s equations, and therefore plays a fundamental role in the theory of classical electromagnetism.

Faraday’s law and relativity[edit]

Faraday’s law describes two different phenomena: the motional EMF generated by a magnetic force on a moving wire (see Lorentz force), and the transformer EMF generated by an electric force due to a changing magnetic field (due to the differential form of the Maxwell–Faraday equation). James Clerk Maxwell drew attention to the separate physical phenomena in 1861.^[21][22] This is believed to be a unique example in physics of where such a fundamental law is invoked to explain two such different phenomena.^[23]

Einstein noticed that the two situations both corresponded to a relative movement between a conductor and a magnet, and the outcome was unaffected by which one was moving. This was one of the principal paths that led him to develop special relativity.^[24]

Applications[edit]

The principles of electromagnetic induction are applied in many devices and systems, including:

Electrical generator[edit]

The EMF generated by Faraday’s law of induction due to relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created. If the wire is connected through an electrical load, current will flow, and thus electrical energy is generated, converting the mechanical energy of motion to electrical energy. For example, the drum generator is based upon the figure to the bottom-right. A different implementation of this idea is the Faraday’s disc, shown in simplified form on the right.

In the Faraday’s disc example, the disc is rotated in a uniform magnetic field perpendicular to the disc, causing a current to flow in the radial arm due to the Lorentz force. It is interesting to understand how it arises that mechanical work is necessary to drive this current. When the generated current flows through the conducting rim, a magnetic field is generated by this current through Ampère’s circuital law (labelled “induced B” in the figure). The rim thus becomes an electromagnet that resists rotation of the disc (an example of Lenz’s law). On the far side of the figure, the return current flows from the rotating arm through the far side of the rim to the bottom brush. The B-field induced by this return current opposes the applied B-field, tending to decrease the flux through that side of the circuit, opposing the increase in flux due to rotation. On the near side of the figure, the return current flows from the rotating arm through the near side of the rim to the bottom brush. The induced B-field increases the flux on this side of the circuit, opposing the decrease in flux due to rotation. Thus, both sides of the circuit generate an EMF opposing the rotation. The energy required to keep the disc moving, despite this reactive force, is exactly equal to the electrical energy generated (plus energy wasted due to friction, Joule heating, and other inefficiencies). This behavior is common to all generators converting mechanical energy to electrical energy.

Electrical transformer[edit]

When the electric current in a loop of wire changes, the changing current creates a changing magnetic field. A second wire in reach of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, d Φ_B / d t. Therefore, an electromotive force is set up in the second loop called the induced EMF or transformer EMF. If the two ends of this loop are connected through an electrical load, current will flow.

Current clamp[edit]

A current clamp is a type of transformer with a split core which can be spread apart and clipped onto a wire or coil to either measure the current in it or, in reverse, to induce a voltage. Unlike conventional instruments the clamp does not make electrical contact with the conductor or require it to be disconnected during attachment of the clamp.

Magnetic flow meter[edit]

Faraday’s law is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called magnetic flow meters. The induced voltage ℇ generated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by:

{\displaystyle {\mathcal {E}}=-B\ell v,}

where ℓ is the distance between electrodes in the magnetic flow meter.

Eddy currents[edit]

Conductors (of finite dimensions) moving through a uniform magnetic field, or stationary within a changing magnetic field, will have currents induced within them. These induced eddy currents can be undesirable, since they dissipate energy in the resistance of the conductor. There are a number of methods employed to control these undesirable inductive effects.

• Electromagnets in electric motors, generators, and transformers do not use solid metal, but instead use thin sheets of metal plate, called laminations. These thin plates reduce the parasitic eddy currents, as described below.
• Inductive coils in electronics typically use magnetic cores to minimize parasitic current flow. They are a mixture of metal powder plus a resin binder that can hold any shape. The binder prevents parasitic current flow through the powdered metal.

Electromagnet laminations[edit]

Eddy currents occur when a solid metallic mass is rotated in a magnetic field, because the outer portion of the metal cuts more lines of force than the inner portion, hence the induced electromotive force not being uniform, tends to set up currents between the points of greatest and least potential. Eddy currents consume a considerable amount of energy and often cause a harmful rise in temperature.^[25]

Only five laminations or plates are shown in this example, so as to show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 to 66 per inch, and brings the eddy current loss down to about one percent. While the plates can be separated by insulation, the voltage is so low that the natural rust/oxide coating of the plates is enough to prevent current flow across the laminations.^[25]

This is a rotor approximately 20mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used to limit parasitic inductive losses.

Parasitic induction within conductors[edit]

In this illustration, a solid copper bar conductor on a rotating armature is just passing under the tip of the pole piece N of the field magnet. Note the uneven distribution of the lines of force across the copper bar. The magnetic field is more concentrated and thus stronger on the left edge of the copper bar (a,b) while the field is weaker on the right edge (c,d). Since the two edges of the bar move with the same velocity, this difference in field strength across the bar creates whorls or current eddies within the copper bar.^[25]

High current power-frequency devices, such as electric motors, generators and transformers, use multiple small conductors in parallel to break up the eddy flows that can form within large solid conductors. The same principle is applied to transformers used at higher than power frequency, for example, those used in switch-mode power supplies and the intermediate frequency coupling transformers of radio receivers.

INFORMATION SOURCE:https://en.wikipedia.org/wiki/Electromagnetic_induction

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Physics Projects with Reports:

1. TO CONSTRUCT A CIRCUIT FOR TOUCH ALARM.
2. EDDY CURRENT {WITHOUT MODEL }
3. PHOTOCONDUCTIVE CELL
4. MUTUAL INDUCTION
5. TO STUDY NPN-TRANSISTOR AMPLIFIER
6. TO CONSTRUCT A ELECTRIC MOTORS (D.C.MOTOR)
7. TO STUDY HOW A TRANSISTOR AMPLIFIER WORK ‘PNP’ AMPLIFIER TRANSISTOR.
8. HOUSEHOLD CIRCUITS
9. AC TO DC CONVERTER (FULL WAVE RECTIFIER)
10. AC TO DC CONVERTER (HALF WAVE RECTIFIER)
11. TO CONSTRUCT A CIRCUIT OF FENCE WIRE BURGLAR ALARM
12. TO SHOW THE PRINCIPLE OF FARADAY’S AND A.C. GENERATOR.
13. THERMOCOUPLE
14. TO STUDY FARADAY’S LAWS-TO FIND THE CHARGE ON AN ELECTRON
15. FARADAY’S LAW’S OF ELECTROLYSIS
16. TO STUDY A POSITIVE FEED BACK CIRCUIT OF AN AUDIO OSCILLATOR (LC OSCILLATOR)
17. HOW DOES AN ELECTRIC GENERATOR WORK
18. TO SHOW THAT A SOLENOID CARRYING AN ELECTRIC CURRENT PRODUCES A MAGNETIC FIELD SIMILAR TO THAT PRODUCED BY A BAR MAGNET.
19. ELECTROCHEMICAL CELL (PRIMARY CELL)
20. BOOLAN LOGIC GATE
21. TO STUDY THE CHARGE AND DISCHARGING OF CAPACITOR IN SERIES
22. WORKING OF POTENTIOMETER
23. KIRCHOFF’S LAW
24. TO DEMONSTRATE THE WORKING OF AN ELECTROLYTIC CAPACITOR BY MEANS OF ITS CHARGING AND DISCHARGING WITH THE HELP OF AN AUDIO OSCILLATOR AND TO STUDY AND COMPARE THE TWO CAPACITORS UNDER SERIES AND PARALLEL COMBINATION.(Z)
25. RADIOACTIVITY AND NUCLEAR REACTIONS.
26. RADIOISOTOPE THERMOELECTRIC GENERATOR.
27. TO CONSTRUCT A CIRCUIT OF SOUND OPERATED SWITCH.
28. TO CONSTRUCT A CIRCUIT OF TIME OPERATED SWITCH.
29. TO CONSTRUCT A CIRCUIT OF SOUND AMPLIFIER.
30. TO CONSTRUCT A CIRCUIT OF A FIRE ALARM.
31. TO CONSTRUCT A CIRCUIT OF CLAP SWITCH.
32. TO CONSTRUCT A CIRCUIT OF TRANSISTOR SWITCH
33. TO FIND OUT OPTICAL ACTIVITY ARISES WHEN THE POLARIZATION AXIS OF LIGHT IS ROTATED AS IT PASSES THROUGH A SUBSTANCE
34. PUSH-PULL AMPLIFIER
35. HARTLEY OSCILLATORS
36. PUSH PULL AMPLIFIER
37. REPORT ON MAGNETIC FIELDS, MAGNETIC FORCES, AND ELECTROMAGNETIC INDUCTION LAWS OF REFRACTION (Z).
38. RAY OPTICS-TO FIND REFRACTIVE INDEX OF THE MATERIAL OF THE PRISM BY TOTAL INTERNAL REFRACTION (Z).
39. TO DEMONSTRATE THE WORKING OF AN ELECTROLYTIC CAPACITOR BY MEANS OF ITS CHARGING AND DISCHARGING WITH THE HELP OF AN AUDIO OSCILLATOR AND TO STUDY AND COMPARE THE TWO CAPACITORS UNDER SERIES AND PARALLEL COMBINATIONS.
40. TO STUDY THE EFFECT OF THE DIAMETER AND THE NUMBER OF TURNS OF THE SPRING ON ITS STRENGTH HAS BEEN INVESTIGATION IN THIS STUDY.(Z)
41. TO FIND OUT THE THERMAL COEFFICIENT OF RESISTANCE FOR A DIVAN SET OF WIRES AND THUS SUGGEST THE WIRE IN WHICH ENERGY LOSS DUE TO HEAT GENERATION IS MINIMUN.(Z)
42. TO SEE THAT WATER CONDUCTS ELECTRICITY BETTER WHEN IMPURITIES ARE ADDED IT. (Z)
43. TO MAKE NOR GATE WITH THE COMBINATION OF TWO GATES. (Z)
44. PASCAL’S LAW AND ITS APPLICATIONS
45. BRIDGE RECTIFIER- A CIRCUIT USING FOUR DIODES TO PROVIDE FULL WAVE RECTIFICATION.CONVERTS AN AC VOLTAGE TO A PULSATING DC VOLTAGE.
46. TO CONSTRUCT A CIRCUIT OF QUIZ BUZZER.
47. TO CONSTRUCT A CIRCUIT OF LASER SECURITY SYSTEM.
48. TO CONSTRUCT A CIRCUIT OF RAIN ALARM.
49. TO CONSTRUCT A CIRCUIT OF WATER LEVEL INDICATOR.
50. THE EFFECT OF TEMPERATURE ON DISPOSABLE AND NON DISPOSABLE BATTERIES
51. TO INVESTIGATE THE EFFECT OF THE FOLLOWING FACTORS ON THE INTERNAL RESISTANCE OF A LACLANCHE CELL.
52. TO CONSTRUCT A CIRCUIT OF OPTICAL SWITCHING.
53. TO CONSTRUCT A CIRCUIT OFCAPACITOR CHARGE OSCILATOR
54. TO CONSTRUCT A CIRCUIT OFCAPACITOR STORAGE LED
55. TO CONSTRUCT A CIRCUIT OF TWO TRANSISTOR OSCILLATOR
56. EXPERIMENTS IN ELECTROCHEMISTRY
57. TO SHOW THE UNIDIRECTION ACTION OF DIODE
58. OPTICAL FIBER COMMUNICATION
59. TO CONSTRUCT A CIRCUIT OF ELECTRONIC EYE

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