7 Key excerpts on "Electric Field Lines"

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  eBook - ePub

  Electrical Engineering

  Fundamentals

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

    (Publisher)

  electrostatic field.

  Each electric charge is surrounded by an electric field. Electric charges interact and affect each other:

  • Like charges repel each other.
  • Unlike charges attract each other.

  A charged particle moves along an imaginary line in the electric field. Such lines of occurring forces are called Electric Field Lines. The following applies for Electric Field Lines:

  • Direction: The Electric Field Lines start at the positive charge (source) and end at the negative charge (sink).
  • Electric Field Lines always start and end on the surface of an electric charge.
  • Electric Field Lines always leave the surface of the electric charge in a right angle.
  • Field lines do not intersect.
  • The denser the field lines, the stronger the force exerted on the charges.

  From a mathematical point of view, the electric field is a vector field of the electric field strength. It assigns a vector for direction and magnitude of electric field strength to each point in the space.

  Figure 1.14: Attracting force and Repulsive force of charges.

  The electric field is the cause for forces exerted on charges. According to the first of Newton’s axioms, a body accelerates as long as force is exerted on it. Moving charge carriers are called current. The sources of an electric field are positive charges, sinks and negative charges. The electric field [Vm−1 ; NC−1 ] is uniform when neither its magnitude nor its direction changes from one point to another.

  1.7.1  Force on charged particle in electric field

  The electric field strength is the measure of the force, a charged body experiences in an electric field. The existing electric field strength at any point in the field can be defined as the force exerted on a positive point unit charge

  Q +

  = 1   A s

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  Electromagnetics Explained

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

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

    (Publisher)

  2 FUNDAMENTALS OF ELECTRIC FIELDS

  THE ELECTRIC FORCE FIELD

  To understand high-frequency and RF electronics, you must first have a good grasp of the fundamentals of electromagnetic fields. This chapter discusses the electric field and is the starting place for understanding electromagnetics. Electric fields are created by charges; that is, charges are the source of electric fields. Charges come in two types, positive (+) and negative (–). Like charges repel each other and opposites attract. In other words, charges produce a force that either pushes or pulls other charges away. Neutral objects are not affected. The force between two charges is proportional to the product of the two charges, and is called Coulomb’s law. Notice that the charges produce a force on each other without actually being in physical contact. It is a force that acts at a distance. To represent this “force at distance” that is created by charges, the concept of a force field is used. Figure 2.1 shows the electrical force fields that surround positive and negative charges.

  Figure 2.1 Field lines surrounding a negative and a positive charge. Dotted lines show lines of equal voltage.

  By convention, the electric field is always drawn from positive to negative. It follows that the force lines emanate from a positive charge and converge to a negative charge. Furthermore, the electric field is a normalized force, a force per charge. The normalization allows the field values to be specified independent of a second charge. In other words, the value of an electric field at any point in space specifies the force that would be felt if a unit of charge were to be placed there. (A unit charge has a value of 1 in the chosen system of units.)

  Electric field = Force field as “felt” by a unit charge

  To calculate the force felt by a charge with value, q, we just multiply the electric field by the charge,

  The magnitude of the electric field decreases as you move away from a charge, and increases as you get closer. To be specific, the magnitude of the electric field (and magnitude of the force) is proportional to the inverse of the distance squared. The electric field drops off rather quickly as the distance is increased. Mathematically this relation is expressed as

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  Fundamental Electrical and Electronic Principles

  • C R Robertson(Author)
  • 2008(Publication Date)
  • Routledge

    (Publisher)

  Fig. 3.3 .

  Fig. 3.3 The following points should be noted:

  1    The lines shown represent the possible paths taken by the positively charged particle in response to the force acting on it. Thus they are called the lines of electric force. They may also be referred to as the lines of electric flux, ψ.

  2    The total electric flux makes up the whole electric field existing between and around the two charged bodies.

  3    The lines themselves are imaginary and the field is three dimensional. The whole of the space surrounding the charged bodies is occupied by the electric flux, so there are no ‘gaps’ in which a charged particle would not be affected.

  4    The lines of force (flux) radiate outwards from the surface of a positive charge and terminate at the surface of a negative charge.

  5    The lines always leave (or terminate) at right angles to a charged surface.

  6    Although the lines drawn on a diagram do not actually exist as such, they are a very convenient way to represent the existence of the electric field. They therefore aid the understanding of its properties and effects.

  7    Since force is a vector quantity any line representing it must be arrowed. The convention used here is that the arrows point from the positive to the negative charge.

  It is evident from Fig. 3.3 that the spacing between the lines of flux varies depending upon which part of the field you consider. This means that the field shown is non-uniform. A uniform electric field may be obtained between two parallel charged plates as shown in Fig. 3.4 .

  Fig. 3.4

  Note that the electric field will exist in all

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  Radiation Detection

  Concepts, Methods, and Devices

  • Douglas McGregor, J. Kenneth Shultis(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 8 Essential Electrostatics

  I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich.

  Michael Faraday

  Numerous radiation detectors rely on the current produced by the motion of mobile charges created by radiation events. Radiation interactions within the detector volume ionize the absorbing medium, thereby creating mobile point charges, usually referred to as charge carriers (because these particles carry the charge through the detector). The detector may be a solid, liquid or gas, within which two or more electrodes are installed. Generally, a voltage is applied to the detector electrodes to move, or drift, the mobile charges across the detector volume to produce the current.

  Electronic detectors range from simple radiation counters to complex radiation spectrometers. The former are used to indicate the presence of ionizing radiation, whereas the latter can also identify the energies and types of radiation. In either case, the fundamental physics of current induction formed by mobile charge carriers applies. Introduced in this chapter are the basic concepts governing charge and current induction in electronic radiation detectors.

  8.1Electric Field

  Consider a point charge of Q coulombs, as shown in Fig. 8.1 . The charge itself has Electric Field Lines emanating from it radially outward (or inward). If a point charge is centered within an imaginary spherical surface, the Electric Field Lines intersect the surface at right angles (perpendicular), with the imaginary surface area 4πr2 , where r is the radius of the sphere. Suppose the number of field lines is denoted by N, then the surface density of field lines becomes N/(4πr2 ) per unit area. It is easy to understand that the electric field line density decreases with r2

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  Pocket Book of Electrical Engineering Formulas

  • Richard C. Dorf, Ronald J. Tallarida(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  26 Static Electric Fields 1.  Unit Vectors and Coordinate Systems The unit vectors for the Cartesian (rectangular) system shown in Figure 26.1(a) are a x, a y, a z and all three vectors are constant. The unit vectors for the cylindrical coordinate system shown in Figure 26.1(b) are a ρ, a ϕ, a z where a z is constant. The unit vectors for the spherical coordinate system shown in Figure 26.1(c) are a r, a θ, a ϕ 2.  Coulomb’s Law For two-point charges Q 1 the source of the field force F, and Q we have the force. on Q as F = Q 1 Q 4 π ∈ 0 R 2 a R (N) where a R is the vector of unit length pointing from Q 1 to Q, ϵ 0 = 10 −9 (36 π), and R is the distance between the charges. FIGURE 26.1. Unit vectors for (a) Cartesian, (b) cylindrical, and (c) spherical coordinates. Electric Field Intensity The electrostatic field intensity is defined as the force on Q when Q = 1 C so E = Q 1 4 π ϵ 0 R 2 a R (V / m) and F = Q E (N) 3.  Gauss’ Law Electric flux. density, D, is D = ϵ 0 E (C / m 2) Gauss’ law states that the net flux of D, or electric flux ψ passing through a surface is equal to the net positive charge enclosed within the surface and thus ψ = ∮ D s ⋅ d S = Q where D s, is the value of D at the surface and dS is the surface element. 4.  Maxwell’s Equation (Electrostatics) The electric flux per unit volume leaving a vanishingly small volume unit is equal to the volume charge density there: div D = ρ where div is divergence and ρ is a volume charge density. Using div D = ∇ · D, we have ∇ ⋅ D = ρ 5.  Poisson’s Equation ∇ · ∇ V = − ρ ∈ or ∇ 2 V = − ρ ε where E = − ∇ V. 6.  Current Density The current density J is related to the electric field E for a metallic conductor as J = σ E where σ is the conductivity of the conductor. The current density J is a convection current J = ρ υ where υ is a velocity vector and ρ is the volume charge density.

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  Fields of Force

  The Development of a World View from Faraday to Einstein.

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

    (Publisher)

  He began by giving a precise definition of a line of magnetic force. It is a line whose tangent is always in the direction of the magnetic force at that point (that is in the direction a small magnetic needle would take at that point), or it can be considered as a line along which no electromagnetic induction takes place if a wire is moved along it. Further, the intensity of force in a region can be represented by the density of lines of force drawn through it. One could fix a ‘unit line’ of force to draw these lines, which would be varying distances apart, depending on the amount of force between them. Such lines may possibly be lines of flow of ether, lines of action at a distance or lines of vibrations. Faraday did not commit himself to any one of these views, but he did state, ‘I am more inclined to the notion that in the transmission of the force there is such an action, external to the magnet, than that the effects are merely attraction and repulsion at a distance.’ 2 In his argument, Faraday then returned to the experiments which originally convinced him of the value of the lines of force view—the unipolar induction experiments. 3 What Faraday wished to show was that the lines of force clearly and exactly represent the phenomena which occur in such experiments. First, he showed that the one rule of electromagnetic induction is that the [total] induced current is directly proportional solely to the number of lines of force cut (for a wire of given conductivity). Second, he showed that the magnetic lines of force go through the magnet itself, and so are always closed; there are no magnetic ‘poles’, but only places where the lines of force happen to enter and leave the magnet

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  Basics of Electromagnetics and Transmission Lines

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

    (Publisher)

  Chapter 1 Static Electric Fields 1.1    Introduction Electrostatic in the sense static or rest or time in-varying electric fields. Electrostatic field can be obtained by the distribution of static charges. The two fundamental laws which describe electrostatic fields are Coulomb’s law and Gauss’s law: They are independent laws. i.e., one law does not depend on the other law. Coulomb’s law can be used to find electric field when the charge distribution is of any type, but it is easy to use Gauss’s law to find electric field when the charge distribution is symmetrical. 1.2    Coulomb’s Law This law is formulated in the year 1785 by Coulomb. It deals with the force a point charge exerts on another point charge; generally a charge can be expressed in terms of coulombs. 1 coulomb = 6 × 10 18 electrons 1 electron charge = − 1.6 × 10 − 19 Coulombs Coulomb’s law states that the force between two point charges Q 1 and Q 2 is along the line joining between them, directly proportional to the product of two point charges, and inversely proportional to the square of the distance between them ∴ F = K Q 1 Q 2 R 2 where K is proportional constant In SI, a unit for Q 1 and Q 2 is coulombs(C), for R meters(m) and for F. newtons(N). K = 1 4 π ∊ 0 where ∊ 0 = permittivity of free space (or) vacuum = 8.854 × 10 − 12 farads / meter = 10 − 9 36 π farads / m K = 36 π 4 π × 10 − 9 = 9 × 10 9 m / farads F = Q 1 Q 2 4 π ∊ 0 R 2 (1.2.1) Assume that the point charges Q 1 and Q 2 are located at (x 1, y 1,. z 1) and (x 2, y 2, z 2) with the position vectors r ¯ 1 and r ¯ 2 respectively. Let the force on Q 2 due to Q 1 be F ¯ 12 which can be written as F ¯ 12 = Q 1 Q 2 4 π ∊ 0 R 2 a ¯ R 12 (1.2.2) where a ¯ R 12 is unit vector along the vector R ¯ 12. Graphical representation of the vectors in rectangular coordinate system is shown in Fig.1.1 Fig

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