Self Induction And Mutual Induction 72nz

1

2

•

S. No.

Table of contents:

Contents

Page No. (From- To)

1.

Introduction of Induction

4

2.

Faraday & Henry experiment

5-8

3.

Self Induction & Mutual Induction

8-14

4.

Applications & Future Use of Self Induction &

15-21

Mutual Induction

5.

Conclusions

22

6.

References

23-24

3

1. INTRODUCTION

 What is INDUCTION? Induction simply means generation or production. In physics, it is the process of generating electric current in the conductor by placing the conductor in the changing magnetic field. It is called because current is said to be induced in the conductor by the magnetic field. When induction occurs in an electrical circuit and affects the flow of electricity it is called inductance. Joseph Henry, an American physicist discovered Induction & investigated how current in one circuit induces current in the another.

4

2. FARADAY

& HENRY EXPERIMENT [III]

It all started through a series of experiments carried out by Faraday & Henry. Faraday’s Law of Induction was discovered through experiments carried out by Michel Faraday in 1831 and by Joseph Henry in the United States at about the same time. The experiments performed by them are described below: •

Experiment 1 When the N-pole of the bar magnet was pushed towards the coil, the galvanometer showed a deflection indicating the presence of electric current in the coil. The deflection continued as long as the bar magnet was in the motion. The galvanometer showed no deflection when the bar magnet was held stationary. Similarly, when the bar magnet was moved away from the coil, the galvanometer showed a deflection but in the opposite direction. Indicating the reversal of the current’s direction. Thus, it was proved by the experiment that it was the relative motion between the magnet and the coil responsible for the generation (production) of electric current.

5

(fig 1)[1]

•

(fig 2)[2]

Experiment 2 In the second experiment, bar magnet was replaced by another coil & was connected to a battery producing a steady current and a steady magnetic field. When the second coil was moved towards the first coil, there was a deflection seen in the galvanometer. When the coil was moved away, the deflection was observed in the opposite direction. Thus it proved that, it was the relative motion between the coils that induced the electric field.

6

(fig 3)[3]

•

Experiment 3 In the third experiment, first coil was connected to a sensitive galvanometer and the second one through a battery through a tapping key. When the key is pressed, galvanometer shoed a deflection & then returned to zero. When it is released, it again showed a deflection but in the opposite direction.

(fig 4)[4]

Thus all the experiments performed by these genius minded scientists brought a conclusion that electric current can be induced in a coil by flux change in another coil or in itself. Induced emf

7

appears in the coil whenever the amount of magnetic flux linked with the coil changes. In both the cases , ΦB is proportional to I.

ΦB α I Where ΦB is the magnetic flux associated with the coil. For a closely wound coil of N turns,

NΦB α I where

NΦB



NΦB α I



NΦB = L I



L

is the magnetic flux linkage.

= NΦB/I

Here L is called the Inductance. Thus inductance is the measure of the flux linkage produced by the inductor per unit of current. Its SI unit is Henry & it depends upon 

Geometry of the Coil



Intrinsic material properties.

8

3. SELF INDUCTION & MUTUAL INDUCTION

I.

SELF INDUCTION: It is the property of the coil due to which the coil

opposes any change in the strength of current flowing through it by inducing an e.m.f in itself. In other words, it is the production of the emf on changing the current in a coil in itself. The property of the self inductance is a particular form of the electromagnetic induction. In the case of self induction, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self induced.

9 (fig 5)[5]



Coefficient of Self Induction

Let I is the current flowing through the coil at any time.

Φ be the magnetic flux linked with all the turns of the coil at that time. We also know that,

ΦαI 

Φ =LI

Here L is a constant of proportionality & is called coefficient of selfinduction or self inductance of the coil. L varies with number of turns of the coil, area of cross-section of the coil & nature of material of the coil.

10

If I =1A Then Φ =L or, L= Φ hence, the coefficient of self induction of the coil can be numerically defined as the amount of magnetic flux linked with the coil when 1 ampere of current flows through the coil. Now, by faraday’s law:

E= -d Φ/dt E= -d(LI)/dt or, E= -LdI/dt

(self induced emf)

11



Self Induction of a Long Solenoid

(fig 6)[6]

The magnetic field around a long solenoid is given by

B = μNI/l Where μ is magnetic permeability of free space, N is the total number of turns in the solenoid. Therefore, magnetic flux through each turn of the solenoid is B X Area of each turn = (μNI/l) A

Therefore, ϕ = (μNI/l) A N

12

But

ϕ = LI

Therefore, LI = (μNNA)/l I.

MUTUAL INDUCTION: When one circuit induces current flow in a nearby circuit, it is known as Mutual Induction. It is the property of two coils due to which each opposes any changes in the strength of current flowing through the other by developing an induced emf.

(fig 7)[5]

(fig 8)[6]

On pressing the key, current in A increases from zero to maximum value. It takes some time to reach to the maximum value. During this time (rise of current) current

13

is continuously increasing hence the magnetic flux associated with the A also increases. Since B is nearby to A, magnetic flux associated with it also increases. Thus an emf is induced in the coil and according to the Lenz’s Law, the induced current in B would oppose increase in current in A by flowing in a direction opposite to the cell current in A. Similarly, on releasing the key, the current in the coil A decreases hence the magnetic flux associated with it decreases. As B is nearby, so magnetic flux associated with B also decreases and hence an induced emf is developed. The direction of the induced current would be in the direction of the cell current so as to oppose the decrease in the current.

(fig 9)[7]

14

(fig 10)[8]



Coefficient of Mutual Induction

Let Φ be the magnetic flux linked with all the turns of the neighbouring coil. I be the current in the coil. We know that,

ΦαI => Φ =MI Here M is a constant of proportionality & is called coefficient of mutual- induction or mutual inductance of the two coils.

15

4.

APPLICATIONS & USE OF SELF and MUTUAL INDUCTION

The applications of this Induction are everywhere. In transformers, AC’s, eddy currents etc. It is only this induction which is basis even for electric guitars which completely changed the face of the whole music world. In details, the applications are discussed below. I.

Inductive Transducers: The inductive pick-up transducers

are mainly used for displacement or position measurement. Example of inductive pick-up based transducer is LVDT ( Linear Variable Differential Transducers) .

16

LVDT is similar to transformer sharing a common core & a primary winding.

(fig 11)[9]

The two secondary coils are connected opposite to each other. The connection is in such a way that the outputs of the two coils are added together simply by connection. The secondary coils are connected in the center of the primary coils. From an Oscillator, an AC current or voltage is applied in the primary coil. The two secondary coils are connected in such a way that when the core is at the centre position, equal voltage signal is induced in both the coils. When the core is displaced right or left, the no. of turns in

17

the secondary coil exposed to the primary coil changes. Thus any movement in the core causes the Mutual Inductance of each secondary coil to vary relative to the primary coil. The variations of mutual inductance of each coil, in effect, induce varied relative voltage in the secondary coils. Since the two secondary coil windings are connected in opposite, as the core moves, the output of one increase and other decrease.

(fig 11)[10]

(fig 12)[10]

18

Fig 12 shows the Cross-Sectional View of LVDT Core and Windings.

II.

Asynchronous AC Motors: An induction motor (or

asynchronous motor) is a type of alternating current motor where power is supplied to the rotor by means of electromagnetic induction. The induction motor was invented by Nikola Tesla in 1882 in . The basic difference between an induction motor and a synchronous AC motor is that in the latter a current is supplied onto the rotor.

(fig 13)

19

The principle of operation of AC motors is similar regarding interaction of the magnetic fields, but commutation is not required. The rotor winding of the asynchronous AC motors have no external voltage applied; rather, voltages are induced in the rotor windings due to the rotating fields around the stator. The rotor rotates at slower speed than the rotary stator fields (called slip) making the induction possible, hence the term asynchronous. Due to this, these are sometime called Induction machines. Induction motors are preferred due to their rugged construction, absence of brushes (which are required in most DC motors) & the ability to control the speed of the motor.

(fig 14)

(A 3-phase power supply provides a rotating magnetic field in an induction motor.)

20 III.

Transformer: Transformers are used to increase or decrease

AC voltages & currents in the circuits The transformer is based on two principles: firstly, that an electric current can produce a magnetic field (electromagnetism) and secondly that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). The basic principle involved in a transformer is Mutual Induction. A change in the current in the primary coil changes the developed magnetic flux. Thus a voltage is induced in the secondary coil by the changing magnetic flux.

(fig 15)[11]

A magnetic field is created by the current ing in the primary coil. The primary and secondary coils are wrapped around a core of very high magnetic permeability. The voltage induced across the secondary coil is

21

-----------------(1)

Where VS is the instantaneous voltage, NS is the number of turns in the secondary coil and Φ equals the magnetic flux. Since the same voltage es through both primary and secondary coils, the instantaneous voltage across the primary is given by

------------------(2)

Dividing equation 1 by equation 2, we get

(it is the basic equation for the stepping up or stepping down.)

22

5. CONCLUSIONS The observations led by Michael Faraday and other scientists revealed another face of our universe how it works. Applications of this Induction is almost everywhere. It is the basis of the many basic amenities required in day-to-day life. For example electric generators that power cities and transportation lines. Induction furnace which is used in industries to melt metals at large scale also makes use of this induction. How about a life without machine or without electricity or even without entertainment? Simply horrible! It’s simply tough for we machine aligned & dependent human to compromise with life without these things. Imagine a life without electricity. Ironically, earth would be Black Hole. Make your head turn around and you will see Induction around you.

23

6.REFERNCES • Websites: 1. http://www.radioelectronicschool.net/files/s/faradyanim.gif 2. http://images.google.co.in/imgres? imgurl=http://faraday.ee.emu.edu.tr/EENG331/faraday1.png&imgrefurl=http://f araday.ee.emu.edu.tr/EENG331/main.htm&usg=__9kgwLtZwX76sZ_lx6v_QtoOn k4I=&h=300&w=500&sz=16&hl=en&start=3&tbnid=VpDIuqE150fZWM:&tbnh =78&tbnw=130&prev=/images%3Fq%3Dfaraday%2527s%2Belectromagnetic %2Binduction%2Bexperiment%26gbv%3D2%26hl%3Den%26sa%3DX

3. http://images.google.co.in/imgres? imgurl=http://www.daviddarling.info/images/electromagnetic_induction.jpg&im grefurl=http://www.daviddarling.info/encyclopedia/E/electromagnetic_induction .html&usg=__QfqqTMyjlWospNDLdWNVXMD4A0g=&h=479&w=500&sz=115& hl=en&start=73&tbnid=s7Na9HB7r2E3XM:&tbnh=125&tbnw=130&prev=/ima ges%3Fq%3Dfaraday%2527s%2Belectromagnetic%2Binduction %2Bexperiment%26gbv%3D2%26ndsp%3D21%26hl%3Den%26sa%3DN %26start%3D63 4. http://images.google.co.in/imgres? imgurl=http://micro.magnet.fsu.edu/electromag/electricity/images/inductance/f araday.jpg&imgrefurl=http://micro.magnet.fsu.edu/electromag/electricity/induc tance.html&usg=__yRu4wuVZn62Iz6eUSEf_XZEeuk=&h=231&w=350&sz=22&hl=en&start=7&tbnid=kqzvy612_scv1M:&tbnh=7 9&tbnw=120&prev=/images%3Fq%3Dfaraday%2527s%2Bexperiment%26gbv %3D2%26hl%3Den%26sa%3DG

24 5. http://www.rfcafe.com/references/electrical/Electricity%20-%20Basic%20Navy %20Training%20Courses/images/Figure%20116.jpg 6. http://www.ndted.org/EducationResources/CommunityCollege/EddyCurrents/Physics/selfinduct ance.htm 7. http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/imgmag/indmut2.gif

8. http://content.tutorvista.com/science/CBSEXScience/Ch534/images/img31.jpeg 9. http://www.me.utexas.edu/~dsclab/labs/forcemotion/Lvdt1.gif 10.http://images.google.com/imgres? imgurl=http://zone.ni.com/cms/images/devzone/tut/a/f841fe69729.gif&imgrefu rl=http://zone.ni.com/devzone/cda/tut/p/id/3638&usg=__6KNl7dFNTBYj2FljaQd uMS9GqZE=&h=276&w=375&sz=12&hl=en&start=11&tbnid=MWHxGZQKtqfj 1M:&tbnh=90&tbnw=122&prev=/images%3Fq%3DLINEAR%2BVARIABLE %2BDIFFERENTIAL%2BTRANSFORMER%26gbv%3D2%26hl%3Den%26sa%3DX 11.http://en.wikipedia.org/wiki/File:Transformer3d_col3.svg

• Books: I.

Resnick R; Halliday D; Krane K. , Physics, John Wiley, Ed 5/Vol 2, 2005, Page-775;776

II.

Resnick R; Halliday D; Walker J. , Physics, John Wiley, Ed 8, 2008, Page805;806;814

III.

Gomber K; Gogia K., Pradeep’s Fundamental Physics, Ed 17, 2008, Page-4/4; 4/11; 4/12; 4/13; 4/14