7 Key excerpts on "Changing Magnetic Field"

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  eBook - ePub

  Rad Tech's Guide to MRI

  Basic Physics, Instrumentation, and Quality Control

  • William H. Faulkner, Euclid Seeram(Authors)
  • 2020(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  2 Fundamental Principles

  Electromagnetism: Faraday's Law of Induction

  Electricity and magnetism go hand‐in‐hand. Whenever an electrical current is produced in a wire, a magnetic field is produced around the wire. As the current in the wire increases, the magnetic field increases. This characteristic is the basic principle behind the construction of resistive and superconductive magnets discussed in Chapter 1 . Magnets or magnetic fields can also be used to induce electrical current in conductors. This principle is known as Faraday's Law of Induction and is written as ΔB/Δt = ΔV Faraday's Law of Induction states that moving a magnet or changing a magnetic field (ΔB) over time (Δt) in the presence of a conductor will induce a voltage (ΔV) in the conductor. As the magnetic field moving through the conductor is increased, the current induced in the conductor is increased. As the time decreases (shortens) – in other words, the more rapid the change in the magnetic field – the more the induced current is increased. Faraday's Law of Induction is the basic principle by which MR signals are induced within the receiver coil.

  Magnetism

  Magnetic Properties of Matter

  All matter has magnetic properties. There are three types of magnetic properties: diamagnetic, paramagnetic, and ferromagnetic.

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  Electrical Engineering

  Fundamentals

  • Viktor Hacker, Christof Sumereder(Authors)
  • 2020(Publication Date)
  • De Gruyter Oldenbourg

    (Publisher)

  5  The magnetic field

  5.1  The term “field”

  Magnetism45 is a physical phenomenon that manifests itself as a force between magnets, magnetised or magnetisable objects and mobile electric charges, like e.g. current-carrying conductors. This force is conveyed through a magnetic field46 (vector field47 ) that, on the one hand, is created by these objects and, on the other hand, affects them. Magnetic fields occur with any movement of electric charges. A “field” is generally defined as a space where physical laws apply to certain circumstances.

  In permanent magnets, magnetism is caused by Ampère’s molecular currents (electrons rotating around the nucleus create a very small spin current and electrons rotate around themselves – electron spin). In permanent magnets the magnetic effects do not cancel each other out. Demagnetising them requires a considerable amount of energy.

  If a magnetic field spreads in a material body, the magnetic properties of the substance influence the intensity of the field. The flux density B does not display the same field strength H as in a vacuum. This is due to the atomic structure of the substances. The electrons rotating around their own axis (electron spin) and the nucleus generate spin currents which create magnetic fields perpendicular to the circular orbit (elementary fields). The elementary fields usually cancel each other out without an additional external magnetic field.

  The magnetic and electric expansion happens at the speed of light and is one of the properties of space. Not only space filled with matter, but also empty space has physical properties.

  • The field strength is the force (amount and direction) that the field exerts on the standard body: the vector field. The field strength is a vector.
  • Field lines are used to visually describe a field; they are only a mental tool and not a physical reality.
  • Magnetic fields arise from mobile charges. The field lines encircle the current

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  eBook - ePub

  Electromagnetics Explained

  A Handbook for Wireless/ RF, EMC, and High-Speed Electronics

  • Ron Schmitt(Author)
  • 2002(Publication Date)
  • Newnes

    (Publisher)

  (The DC magnetic field can be supplied by permanent magnets or by an electromagnet.) With a DC field applied, ferrites become anisotropic; that is, their magnetic properties are different in different directions. Simply stated, the DC field causes the ferrite to be saturated in the direction of the field while remaining unsaturated in the other two directions. Voltage-controlled phase-shifters and filters as well as exotic directional devices such as gyrators, isolators, and circulators can be created with ferrites in the microwave region. MAXWELL’S EQUATIONS AND THE DISPLACEMENT CURRENT In the 1860s, the British physicist James Clerk Maxwell set himself to the task of completely and concisely writing all the known laws of electricity and magnetism. During this exercise, Maxwell noticed a mathematical inconsistency in Ampere’s law. Recall that Ampere’s law predicts that a magnetic field surrounds all electric currents. To fix the problem, Maxwell proposed that not only do electric currents, the movement of charge, produce magnetic fields, but changing electric fields also produce magnetic fields. In other words, you do not necessarily need a charge to produce a magnetic field. For instance, when a capacitor is charging, there exists a changing electric field between the two plates. When an AC voltage is applied to a capacitor, the constant charging and discharging leads to current going to and from the plates. As I discussed in Chapter 1, although no current ever travels between the plates, the storing of opposite charges on the plates gives the perceived effect of a current traveling through the capacitor. This virtual current is called displacement current, named so because the virtual current arises from the displacement of charge at the plates

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  Essentials of MRI Safety

  • Donald W. McRobbie(Author)
  • 2020(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Figure 2.3 ). The induced electric field is sometimes called “conservative” as it involves no external static charges. Faraday’s Law is also responsible for the detection of the MR signal in an RF receive coil – so it’s important!

  Figure 2.3

  Electric fields induced by a time‐varying magnetic field form complete loops (unless there are static electrical charges present); dB/dt is into the page.

  Electromagnetic waves

  Maxwell’s fourth equation, or Ampere’s Law, tells us that magnetic fields can be generated both by electric currents and by time‐varying electric fields, allowing for the existence of electro‐magnetic waves – everything in the electromagnetic spectrum: gamma rays, X‐rays, ultraviolet, visible light, infrared, microwaves, and radiowaves (Figure 2.4 ). It has consequences for the more “wave‐like” behavior of the B1 excitation field at higher frequencies. It also results in field exposures from the gradients being higher than intuitively anticipated.

  Figure 2.4

  Electromagnetic wave: the magnetic and electric fields are orthogonal to each other and to the direction of propagation.

  Generating magnetic fields

  Maxwell’s equations teach us that a magnetic field (we shall drop the proper term “flux density”) is generated by an electrical current. In this section we consider the generation of magnetic fields from conductors and coils in various simple configurations. Further detail is given in Appendix 1 .

  B field from a long straight conductor

  If we have a straight wire and pass a current I along it, then the magnetic field generated will have circular field lines (Figure 2.5 ). The direction of the field lines can be determined by the “right hand rule”, namely that if your right hand’s thumb represents the direction of current flow, then your cupped fingers will indicate the circular B field direction, denoted Bθ . The magnitude of the field at a radial distance r from the wire is proportional to 1/r. The subscript θ (from polar coordinates‐ see Appendix 2

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  eBook - ePub

  Energy Medicine - E-Book

  The Scientific Basis

  • James L. Oschman(Author)
  • 2015(Publication Date)
  • Churchill Livingstone

    (Publisher)

  Chapter 8 .

  Electricity from Magnetism: Faraday’s Law of Induction

  About 11 years after Ørsted’s important discovery in Denmark, another important finding took place simultaneously in England and America. Electromagnetic induction is the reverse of Ampère’s law, i.e., magnetic fields can cause currents to flow through conductors. Electromagnetic induction was discovered by the English chemist and physicist, Michael Faraday in 1831, and, independently and at the same time, by an American scientist, Joseph Henry (Figure 2.7 ). The resulting law of physics is known as Faraday’s law of induction because Faraday published his results before Henry. Note from Figure 2.7C the inductive effect with a single loop of wire. Coils with larger numbers of turns increase the inductive effect. This is mentioned because many of the tissues in the human body have a helical aspect to them, and therefore have the possibility of utilizing the phenomenon discovered by Faraday and Henry. The unit of capacitance, the farad, is named after Michael Faraday. Capacitance will become significant and will be defined when the oscillator is described.

  Figure 2.7 In 1831, Michael Faraday (A) in England and Joseph Henry (B) in the United States independently discovered that a moving magnetic field will induce a current flow through a wire without touching it (C). Magnetism can be converted into electricity.

  The unit of inductance, the henry, is named after Joseph Henry. Again, inductance will be defined in connection with the oscillator. Henry’s work on the electromagnetic relay was the basis of the electrical telegraph, invented independently by Samuel Morse and Charles Wheatstone. Induction and coils provide the basis for important devices such as solenoids, which produce much stronger magnetic effects than a straight wire, and transformers composed of two coils, a primary and a secondary, which can step voltages up or down (Figure 2.8 ). We shall see that induction also explains how the electrical fields from the hands of a therapist, which are caused in part by the electric field of the heart flowing through the circulatory system, can induce the flows of microcurrents in the tissues of a patient and how certain energy medicine devices can likewise induce currents in tissues. These phenomena will be discussed in more detail in Chapter 15

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  eBook - ePub

  Fields of Force

  The Development of a World View from Faraday to Einstein.

  • William Berkson(Author)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  all matter in a force field. For with the discovery of electromagnetic induction, Faraday was confirmed in his habit of mind, which was to think of each experiment's consequences for the whole world picture.

  Now Faraday's new metaphysical view was clear to him. The first step, as I suggested earlier, was the hypothesis of non-central forces and the consequent idea that the force field is real. The second step, the idea that all changes in the field take time to move from place to place, was then taken. It was prompted by the theory that electromagnetic induction of current in a wire is proportional to the rate at which the lines offeree cut the wire. Faraday saw that it was a consequence of this theory that the lines of force move away from a wire where the current is increasing and that their motion has observable effects—the induction of a current in a neighbouring wire.

  Where his new view differed from the Newtonian world view now became clear to him in a rush. The principal points of divergence seemed: (1) there is no action at a distance, but only action of one force point of the (universal) field on other contiguous points; (2) any material body in a force field has its configuration of forces altered as a result of the field, of which it is part. Faraday was now faced with the problem: How could these new ideas be tested against the old Newtonian theories? The attempt to find such tests occupied the rest of his life. The search was very fruitful, though it was never successful in achieving its main aim, which was to show that field theory had crucial advantages over the atoms and empty space view of Newton. The next chapter tells the story of this search.

  Before we turn to this story, however, let us see what were Faraday's ideas, in his own words, of the important problems opened up by the discovery of electromagnetic induction. Half a year after his discovery of electromagnetic induction Faraday wrote a note, which was sealed and deposited at the Royal Society, to establish priority of his new ideas arising from his consideration of electromagnetic induction. The new feature of his views, which Faraday emphasizes in this note, is that action through the field takes time . It was only in his last years, almost thirty years after this note was written, that Faraday discovered that this could really be the crucial experiment he sought. The note reads thus:30

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  eBook - ePub

  Basics of Electromagnetics and Transmission Lines

  • G. Jagadeeswar Reddy, T. Jayachandra Prasad(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  3

  Maxwell’s Equations for Time Varying Fields

  3.1    Introduction

  The static electric fields are represented by Ē (x, y, z) and static magnetic fields are represented by

  H ¯

  (

  x , y , z

  )

  . We know that the static electric fields are generated by static charges and static magnetic fields are generated by moving charges or steady currents. In static electromagnetic fields, the static electric field and static magnetic field are independent. The time varying electric field can be represented with Ē(x, y, z, t) and time varying magnetic field can be represented with

  H ¯

  (

  x , y , z , t

  )

  . In time varying electromagnetic fields, the electric and magnetic fields are interdependent. These fields are generated by accelerated charges or the time varying current waveforms that are shown in Fig.3.1 .

  Fig. 3.1 Current waveforms

  We can also call time varying electromagnetic fields as electromagnetic waves as they are produced by time varying currents.

  3.2    Faraday’s Law and Transformer EMF

  The two basic concepts that we are going to study in time varying electromagnetic waves are (i) induced emf according to Faraday’s law (ii) displacement current. According to Faraday’s law in a closed circuit the induced emf is equal to the time rate of change of magnetic flux linkage

  i .e . , V e m f = − d λ d t

  (3.2.1)

  If each turn of the circuit carries flux ‘ψ’ then flux linkage λ = Nψ, then induced emf is

  V e m f = − N d ψ d t

  (3.2.2)

  Where −ve sign indicates, the induced emf opposes the magnetic flux linkage. This is called Lenz’s law.

  So far we know that the electric fields are generated by static charges. But there are other sources that generate electric fields, they are called emf produced fields the sources of generating emf produced fields are Electric generator, Batteries and Fuel cells etc. All these convert non electrical energy into electrical energy. Let us consider a circuit which has battery as shown in Fig.3.2 .

  Fig. 3.2

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