Magnetic Flux

7 Key excerpts on "Magnetic Flux"

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Chapter 16 .

  As before, the total flux from a source is also used as a measure of the strength of the source. Thus the flux concept is carried over to the case of magnetic fields simply by defining the total Magnetic Flux

  (ΦM )

  from a pole as being equal to the magnetic pole strength, that is

  Even when the magnet is not long and thin (such as in Figure 18.2 (a)), the pole strength can be defined as the total flux emanating from the N pole end (or sinking at the S pole).

  The intensity at some point in a magnetic field can be measured in terms of the Magnetic Flux per unit area at that point. Thus a vector quantity, called the Magnetic Flux density is defined by

  where

  ΔΦM

  is the Magnetic Flux through an area

  ΔA

  which is perpendicular to the field lines through the point and is a unit vector tangential to the field lines, that is perpendicular to ΔA, as illustrated in Figure 18.18 . The SI unit of Magnetic Flux density is

  Wb m−2

  , called the tesla (after Nikola Tesla 1856–1943), that is,

  1 tesla = 1 Wb m−2 = 1 T

  .1

  Figure 18.18

  ΔΦM

  is the Magnetic Flux through the area

  ΔA

  . The Magnetic Flux density B is directed perpendicularly to the area

  ΔA

  , that is, tangentially to the local magnetic field line.

  From the definitions presented above, both the Magnetic Flux density B and the magnetic field strength H at a point in a non‐conducting medium are directed along the tangent to the local magnetic field line through that point ( in Figure 18.18 ). Thus B is parallel to H, that is

  The value of

  μ

  depends on the nature of the medium in which the currents and/or magnetic poles which give rise to the magnetic field and the field itself are immersed. The quantity

  μ

  , therefore, is a property of the medium and is called the permeability of the medium. The distinction between B and H will become clearer in Section 19.9

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  eBook - ePub

  Engineering Science

  • W. Bolton(Author)
  • 2015(Publication Date)
  • Routledge

    (Publisher)

  Chapter 14 Magnetic Flux

  14.1 Introduction

  This chapter follows on from the discussion of magnetism in Chapter 10 and considers in more detail electromagnetic induction. Magnetic lines of force can be thought of as lines along which something flows, this being termed flux . When the Magnetic Flux linked by a coil changes then an e.m.f. is induced.

  We also look at the effect of the materials through which lines of Magnetic Flux pass. This is important since most devices employing magnetism involve the use of materials such as iron or steel in their construction. When any material is placed in a magnetic field, the extent to which the magnetic field permeates the medium when compared with what would happen in a vacuum is known as the relative permeability. For a material termed ferromagnetic, such as iron, there is a tendency for the lines of Magnetic Flux to crowd through it and it has a high relative permeability (Figure 14.1(a) ). An important consequence of this high permeability of iron is that an object surrounded by iron is almost completely screened from external magnetic fields as the Magnetic Flux lines crowd through the iron (Figure 14.1(b) ).

  Finally in this chapter we look at the forces experienced by current-carrying conductors when in magnetic fields, this being the basic principle behind d.c. motors.

  Figure 14.1 (a) A piece of iron in a magnetic field, (b) screening

  14.2 Electromagnetic induction

  We can represent Faraday’s law and Lenz’s law for electromagnetic induction (see Chapter 10 ) as:

  induced e.m.f. e ∝ – (rate of change of flux Φ with time t )

  The minus sign indicates that the induced e.m.f. is in such a direction as to oppose the change producing it. We can put the constant of proportionality as 1 and write rate of change of flux as dΦ /dt :

  The unit of flux is the weber (Wb). If the flux linked changes by 1 Wb/s then the induced e.m.f. is 1 V. For a coil with N turns, each turn will produce an induced e.m.f. and so the total e.m.f. will be the sum of those due to each turn and thus:

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  eBook - PDF

  Fundamentals of Electrical Engineering, Part 1

  • S. B. Lal Seksena, Kaustuv Dasgupta(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  6.2 Concept of Magnetic Flux Flow We have known so far that in an electric circuit we need to have at least one active source and at least on passive element. A potential difference is created across the passive element by the active source due to which an electric current flows through the passive component. Let us depict such a basic 6 MAGNETIC CIRCUIT Fig. 6.1: Basic electric circuit E R I Magnetic Circuit 301 electric circuit having one energy source or emf source E, a voltaic cell and one resistor having resistance R, as shown in Fig. 6.1. The cell is supplying an electro motive force (emf ) to the circuit. It drives the current (I) to flow through resistance R. By the current flow we actually mean a continuous current is established in the circuit. According to Ampere's law an electric field will be generated due to this current flow. Now let us consider another situation as depicted in Fig. 6.2. In this case a current carrying coil is wounded on a magnetic core. If we set a current into the coil the magnetic core will be magnetic cell and form an electromagnet. In other words the coil will inject a driving force in the system to establish a unidirectional Magnetic Flux. Comparing with the last case we can say a Magnetic Flux is flowing through the core of magnetic material. This Magnetic Flux creates a magnetic field. The coil here acts like an energy source and the core acts like a magnetic conductor. The circuit through which a current is allowed to pass is the basic magnetic circuit. The active component or the energy source of the magnetic circuit is a magnetic coil. The current through the coil establishes the flux. 6.3 Ampere's Law and Magnetic Circuit: MMF We know from Ampere's circuital law that the total work done is the total closed loop integral of the magnetic field: From Ampere’s Law we can write W = ∮ – H. — dℓ …………. 6.1 or, W = 1 – μ ∮ – B. — dℓ …………. 6.2 For a long solinoid B = — μ NI L ………….

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  eBook - PDF

  Handbook of Magnetic Measurements

  • Slawomir Tumanski(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  μ .and. magnetization. M .of.a.material . .In.free.space,.there.is.no. magnetization. and. permeability. is. equal. to. μ 0 ,. so. the. magnetic.flux. Φ .caused.by.a.magnetic.field. H .is . F = μ 0 A H . (2 .12) The unit of Magnetic Flux is 1 Wb (weber) or Vs . The.magnetic.flux.density. B .(sometimes.also.called.as. a.magnetic.induction).is.a.more.commonly.used.quan-tity.and.is.equal.to . B A = Φ . (2 .13) * . According. to. Einstein’s. theory. of. relativity,. for. the. stationary. observer,. this. statement. is. obvious,. but,. if. the. observer. is. mov-ing.with.the.charge,.the.effects.of.magnetic.and.electric.field.are. reversed. .So.we.can.say.that.the.magnetic.field.is.a.relativistic.cor-rection.to.the.electric.field.(see.Jiles.1998) . From.(2 .12) .and.(2 .13), .we.can.see.that.in.a.free.space.the. relationship.between.magnetic.field.strength. H .and.flux. density. B .is . B H = μ 0 . (2 .14) The unit of Magnetic Flux density is 1 T (tesla) . The. presence. and. direction. of. magnetic. flux. can. be. easily.detected.with.iron.filings.(Figure.2 .3). According.to.Equation.2 .14, .in.a.free.space,.the.relation-ship.between.the.magnetic.field.strength. H .and.the.flux. density. B .is.linear.(constant.factor. μ 0 ). .For.this.reason,.it. does.not.matter.which.quantity.is.used.as.the.reference. source. .Independently.of.what.is.the.cause.and.what.is. the.result,.most.often,.the.flux.density.standard.is.used. as. a. reference. for. the. magnetic. field . . The. standard. is. defined.by.the.relationship.between.the.magnetic.field. generated.by.an.electric.current.and.mechanical.force . . A Magnetic Flux density B of 1 T generates a force of 1 N (per-pendicular to the direction of the Magnetic Flux) for each 1 m of a conductor carrying a current of 1 A .(Figure.2 .4a). We.can.also.determine.the.flux.density.according.to.

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  eBook - ePub

  Understanding DC Circuits

  • Dale Patrick, Stephen Fardo(Authors)
  • 1999(Publication Date)
  • Newnes

    (Publisher)

  B ). As a magnetizing force increases, so does flux density. Flux density is the number of lines of force per unit area of a material. An increase in flux density occurs until magnetic saturation is reached. This saturation point depends on the type of material. At the saturation point, the maximum alignment of domains takes place in the material.

  Figure 4-16 Magnetization or B -H curve.

  Magnetizing force (H) is measured in oersteds . The basic unit is the number of ampere-turns per meter of length. Flux density (B) is the amount of Magnetic Flux per unit area. The unit of flux density is the gauss per square centimeter of area.

  Self-Examination

  5.  _____ is magnetism caused by current flow.

  6.  The polarity of an electromagnet may be determined by means of applying the_____.

  7.  The three basic parts of an electromagnet are _____, _____, and _____.

  8.  Three ways to increase the strength of an electromagnet are _____, _____, and

  9.  _____ is the ease with which a material conducts magnetic lines of force.

  Answers

  6.  Electromagnetism

  7.  Left-hand rule

  8.  Core, windings, voltage (current) source

  9.  More turns (windings), more current flow (voltage), better core material

  10.  Permeability

  EXPERIMENT 4-1 THE NATURE OF MAGNETISM

  Magnetism is one of the longest-known natural forces. It was first discovered and used in ancient cultures as a curiosity. Many believed that this force was magic and therefore to be feared. The first magnets used were natural magnets called lodestones and were first put to practical use in navigation. Someone discovered that when these devices were suspended by a string and allowed to move freely, they would always align themselves to point to the north. Thus natural magnetism was first used for compasses.

  Much later it was discovered that magnetism could be used to produce an electric current and that an electric current could be used to produce a magnetic field. This relation makes a knowledge of magnetism extremely important.

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  Electromagnetism for Engineers

  • Andrew J. Flewitt(Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  (4.5) and (4.6) shows that J M = |M| (4.7) or in other words, the magnetization is the effective surface current whose effect would be to produce the observed magnetic dipole moment of the material. Let us assume that we have a material in which all of the microscopic magnetic dipole moments are randomly aligned when no external field is applied. Inspection of the expres- sions for the Magnetic Flux density produced by a dipole (Eq. (4.2)) and the magnetization due to the dipoles (Eq. (4.3)) would lead us to expect that the magnetization induced is pro- portional to B/𝜇 0 . The constant of proportionality 𝜒 B is called the magnetic susceptibility, so that M = 𝜒 B B 𝜇 0 (4.8) It is analogous to the electric susceptibility (Eq. (2.9)) and is also similarly dimensionless. We now introduce a new quantity: the magnetic field H. This is analogous to the elec- tric field E, and, like the electric field, it is a measure of the actual field that will produce a real force acting on a moving charge in the presence of the field. The Magnetic Flux den- sity B that we have been using throughout Chapter 3 is like the electric flux density D; it is simply a mathematical construction which makes calculation of magnetic fields more straightforward. For the simple magnetic material which we have been considering where the linear rela- tion of Eq. (4.8) between magnetization and applied Magnetic Flux density is valid, a simple linear relation also holds between B and H given by B = 𝜇 0 𝜇 r H (4.9) 54 Electromagnetism for Engineers which is analogous to the relationship between electric field and electric flux density (Eq. (2.15)). We have already defined 𝜇 0 as being the permeability of free space (see Section 3.3), while 𝜇 r is known as the relative permeability and is a material-dependent quantity. The relative permeability of free space is unity. Together, the quantity 𝜇 0 𝜇 r is known simply as permeability.

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  Introductory Physics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  Electromagnetism: the relationship between magnetic and electric fields Faraday's Law: Electric force due to a changing B -field A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in the coil). This is known as Faraday's law and forms the basis of many electrical generators and electric motors. Mathematically, Faraday's law is: where is the electromotive force (or EMF , the voltage generated around a closed loop) and Φ m is the Magnetic Flux —the product of the area times the magnetic field normal to that area. (This definition of Magnetic Flux is why B is often referred to as Magnetic Flux density.) The negative sign is necessary and represents the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it. This phenomenon is known as Lenz's Law. ________________________ WORLD TECHNOLOGIES ________________________ This integral formulation of Faraday's law can be converted into a differential form, which applies under slightly different conditions. This form is covered as one of Max-well's equations below. Maxwell's correction to Ampère's Law: The magnetic field due to a changing electric field Similar to the way that a changing magnetic field generates an electric field, a changing electric field generates a magnetic field. This fact is known as ' Maxwell's correction to Ampère's law' . Maxwell's correction to Ampère's Law bootstrap together with Faraday's law of induction to form electromagnetic waves, such as light. Thus, a changing electric field generates a changing magnetic field which generates a changing electric field again. Maxwell's correction to Ampère law is applied as an additive term to Ampere's law given above.

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