7 Key excerpts on "Electric Field Energy"

• 

  eBook - ePub

  Electrical Engineering

  Fundamentals

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

    (Publisher)

  4  The stationary electric field

  To separate charges energy is necessary; this energy is stored in the space between the separated charges. The resulting energy space is referred to as electric field. In this field, forces are exerted onto charge carriers. Electrically charged objects are surrounded by an electric field, which represents the state of a certain space (e.g. between electrically charged objects). Said state is characterised by the electric charges that are affected by a force as soon as they enter its space. The electric field strength E measures the force that affects a charged object in an electric field.

  The electric field strength at a certain point within the field is defined as the force exerted on a positive point unit charge

  Q +

  = 1   A

  s or C. The mechanical force F as well as the electric field strength E are vector quantities:

  E ⃗

  =

  F ⃗

  Q +

  E =

  V m

  Field types

  The pattern of the electric field lines strongly depends on the geometric arrangement of charges. Field lines always enter or exit the charge carrier vertically.

  Radial symmetric field

  Figure 4.1: Field line path of a charged sphere.

  Homogeneous field

  Figure 4.2: Field line path between two charged plates.

  Displacement work

  The force F depends on the field strength E and the quantity of electric charge Q.

  Energy level

  If a charge is moved using work against the field force, it subsequently has a higher energy level.

  Electric potential

  To obtain information on the possible (work) potential of an electric field, the potential must relate to the charge (potential per unit charge). The reference potential can be determined arbitrarily. Usually, the negative electrode is defined as zero potential. A surface with same electric potential at every point is called an equipotential surface.

  Voltage

  When energy is gained or lost, a charge is transferred from an electric potential 1 to another potential 2. The potential difference is called voltage V (corresponds to the striving for balance of separated charges). Voltage is also referred to as potential difference.

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  Energy Medicine - E-Book

  The Scientific Basis

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

    (Publisher)

  This electric field influences other electrically charged objects. There are two ways of describing the influences of fields and the ways they interact with each other. One perspective is that objects have properties that modify the space around them such that another object entering that space will have a force exerted upon it. A second perspective does not require the concept of force: Objects have properties that modify the space around them such that another object entering that space will experience a change in its motion. In the case of the electron, shown in Figure 2.2, the lines of force reveal the direction of motion a positive test charge would experience when brought into the space around the electron. Specifically, since opposite charges attract, the positive test charge will be drawn towards the center of charge of the electron. Figure 2.2 The electric field of a stationary electric charge. Note that the charge is imaged as a point in space. This is a simplification that has made it easier to calculate charge interactions. However, there are other valuable perspectives on the nature of the electric charge that will be discussed in this chapter. With regard to the image of the electron shown in Figure 2.2, recognize that the view of the electron as a point in space is but one of several models of the electron and other charged particles. What is an Electron? Much of the discussion that follows will concern the behaviour of electrons and other charged particles. We shall see that when a charge moves, magnetic fields are produced. And we will also see that the opposite is true: Magnetic fields alter the motions of nearby charges. These principles are profoundly important for energy medicine. Many of the techniques used in energy medicine look like New-Age hocus-pocus until they are viewed through the discerning eyes of the physicist and biophysicist

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  Electromagnetics Explained

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

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

    (Publisher)

  * Without any aether, there is no way to measure absolute velocity. All movement is therefore relative.

  Figure 2.2 Two balls attached by a spring. The spring exerts an attractive force when the balls are pulled apart.

  VOLTAGE AND POTENTIAL ENERGY

  A quantity that goes hand in hand with the electric field is voltage. Voltage is also called potential, which is an accurate description since voltage quantifies potential energy. Voltage, like the electric field, is normalized per unit charge.

  Voltage = Potential energy of a unit charge

  In other words, multiplying voltage by charge gives the potential energy of that charge, just as multiplying the electric field by charge gives the force felt by the charge. Mathematically we represent this by

  Potential energy is always a relative term; therefore voltage is always relative. Gravity provides a great visual analogy for potential. Let’s define ground level as zero potential. A ball on the ground has zero potential, but a ball 6 feet in the air has a positive potential energy. If the ball were to be dropped from 6 feet, all of its potential energy will have been converted to kinetic energy (i.e., motion) just before it reaches the ground. Gravity provides a good analogy, but the electric field is more complicated because there are both positive and negative charges, whereas gravity has only positive mass. Furthermore, some particles and objects are electrically neutral, whereas all objects are affected by gravity. For instance, an unconnected wire is electrically neutral, therefore, it will not be subject to movement when placed in an electrical potential. (However, there are the secondary effects of electrostatic induction, which are described later in the chapter.)

  Consider another example, a vacuum tube diode, as shown in Figure 2.3

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  Energy Storage

  A New Approach

  • Ralph Zito, Haleh Ardebili(Authors)
  • 2019(Publication Date)
  • Wiley-Scrivener

    (Publisher)

  Imagine a charged particle at a certain voltage. The electrical or electrostatic energy (or work) associated with this particle can be calculated by multiplying its charge (in coulomb) by the voltage (in volt):

  (2.18)

  Now, imagine two particles with respective charges q1 and q2 (coulomb). The electrostatic potential energy U (joules) between the two bodies depends not only on their charges, but also the distance between the bodies r (meters) expressed as

  (2.19)

  where єo is the permittivity in vacuum equal to 8.854 187 817 … ×10–12 F m–1 .

  Now, instead of a charged particle, let us take a look at a charged plate, as in the case of a capacitor. A classical capacitor consists of an insulator or dielectric material that is placed between two charged parallel plates. The capacitance of a classical parallel plate capacitor is expressed as

  (2.20)

  where C is the capacitance (Farad or F), єo is the permittivity in space equal to 8.854 × 10–12 F/m, єr is the relative permittivity of the material between the plates, also known as the dielectric constant of the material, A is the area of the plates (m2 ), and d is the distance between the plates (m).

  To determine the energy stored in a capacitor, we will first start with the basic relation between the capacitance, charge and voltage. In an ideal capacitor, the capacitance is assumed to be constant and is expressed as following:

  (2.21)

  where Q is the charge on the capacitor plates (or electrodes), and V is the voltage across the plates.

  A strategy to compute the total energy stored in a capacitor is to first calculate the energy of an infinitesimal amount of charge added to the capacitor plate. Then, we can integrate the term over the total charge on the plate and find the total energy stored in a capacitor.

  Let’s define the differential energy, dU that is associated with an infinitesimal amount of charge, dq. This small charge dq is added to the capacitor plate, at a certain voltage, V(q), as depicted in Figure 2.5

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  Radiation Detection

  Concepts, Methods, and Devices

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

    (Publisher)

  The remaining volume integral can be converted to an integral over the surface S of V by using Gauss’ divergence theorem [Riley et al. 2006] to obtain ∫ ∫ S E ⋅ n ^ d S = Q t o t a l ϵ o, (8.9) where n ^ is the outward unit normal to the surface S. Equation (8.6), or the alternative form Eq. (8.7), are usually referred to as Gauss’ law in differential form, while Eq. (8.9) is Gauss’ law in integral form. 8.2 Electrical Potential Energy An electric field causes mobile charges to move, hence an electric field does work on a mobile charge. The work required to move the particle from position r 1 to position r 2 is given by W = ∫ r 1 r 2 F ⋅ d l = ∫ r 1 r 2 F cos ⁡ θ d l, (8.10) where F is the force vector applied to the particle, d l is a differential length along the direction of travel, and θ is the angle between these two vectors. Coulomb’s law states that the force on a particle at r ′ with charge q ′ from a second particle at r with charge q is F = Q Q ′ (r − r ′) 4 π ϵ o | r − r ′ | 3 with magnitude F = Q Q ′ 4 π ϵ o r 2, (8.11) where r is the distance between the charges. Consider the electric field of a point charge Q shown in Fig. 8.1. If another point charge Q ′ is placed in the electric field of the first charge Q, then the electric field of Q exerts a force on Q ′, and the electric field of Q ′ exerts an equal force on Q. In Fig. 8.5, a single charge Q ′ is moving in the electric field of a second charge Q from position r 1 to position r 2 across the field lines of Q. In the limit of decreasing angles between field lines, Δ ω → dω, Δ l → dl, Δ r → dr, and θ 1 = θ 2 = θ. From Fig. 8.5, the relationship between the differential distance traveled dl and the differential change in distance between the charges dr is cos ⁡ θ d l = d r. (8.12) Substitution of Eq. (8.12) into Eq

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  Instrumentation

  An Introduction for Students in the Speech and Hearing Sciences

  • T. Newell Decker, Thomas D. Carrell(Authors)
  • 2004(Publication Date)
  • Psychology Press

    (Publisher)

  1 Introduction to Basic Electricity

  Almost without exception, when a person decides to use an instrument, it must first be connected to an electrical outlet. Because electricity is almost always available for our use, we tend to take it for granted, never questioning what it is or from where it comes. There are, however, some fundamental electrical concepts that are important to the overall understanding of clinical and laboratory equipment as it is discussed in later chapters of this book. But even more important, these concepts should be understood in order to operate instruments safely. This chapter contains a simplified discussion of where electricity comes from, what its basic parameters are, and how it can be used safely. Some simple equations and formulas illustrate the basic concepts, and you are encouraged to study them.

  ELECTRICAL FIELDS AND CHARGES

  Atoms are no longer thought of as the smallest particle of an element. We now know that atoms are made up of much smaller particles, some of which are: electrons , protons , and neutrons . Electrons and protons are the stuff of which electrical energy is made. Electrons have an electrical charge with a negative value, whereas protons have an electrical charge with a positive value. Both protons and electrons are of fundamental importance to the presence of electricity. Because neutrons have a neutral or zero charge, we will not be concerned with them in this chapter.

  Figure 1.1 demonstrates a basic characteristic of electrical charges. Charges that are of the same value or sign will repel each other; charges that are of dif-

  FIG. 1.1. Polarity of electrical charges showing that different charges attract and similar charges repel.

  ferent values or signs attract. Most of us have demonstrated an analogous property to ourselves with magnets. If we hold the south poles of two magnets together and then release them, the magnets jump apart. If, on the other hand, we hold the south pole of one magnet and the north pole of the other magnet close together and then release them, they jump together. There is a field of force (attraction) between the magnets just as there is with the electrical charges. This force field pushes like charges away and attracts dissimilar charges. By convention, this field of force is usually visualized from the perspective of the positive electrical charge. Figure 1.2

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  The Special Theory of Relativity

  • David Bohm(Author)
  • 2003(Publication Date)
  • Routledge

    (Publisher)

  Similarly, an electric current I flowing 2 through a coil of inductance L has energy LI 2 /2, which is conserved if there is no resistance, and which can be transformed into a corresponding quantity of mechanical energy with the aid of a motor, and into heat energy with the aid of a resistance. We emphasize then that energy is always an invariant, but transformable, aspect and function of some kind of movement and never appears as an independently existing substance. Even potential energy is defined just as the capacity for doing work, i.e., for creating a corresponding movement, measured in terms of mechanical, electrical, thermal, or other forms of energy. In the earlier stages of the development of physics, it was in principle possible to think of all movement as a quality or property of some kind of particles. With the discovery that mass (and even the particles themselves) can be “annihilated,” with the liberation of equivalent amounts of energy, this way of thinking ceased to be tenable. But if the energy does not belong to such particles, how then are we to conceive of it? If energy has meaning only as a relatively invariant function of movement, and if there are no basic and permanent constituents of the universe which possess this movement, what can we mean by the terms “energy” and “movement”? To answer these questions it will be helpful to begin by introducing a distinction between two kinds of energy. On the one hand, there is the energy of outward movement which occurs on the large scale, for example, when a body changes its position or orientation as a whole. On the other hand, there is the energy of inward movement, for example, the thermal motions of the constituent molecules, which cancel out on the large scale. It is characteristic of inward movement that it tends to be to-and-fro, oscillating, reflecting back and forth, and so on

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