8 Key excerpts on "Electric Force"

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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)

  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

  where r is the distance from the source and q is the value of the source charge. Putting our two equations together gives us Coulomb’s law,

  where

  q1

  and

  q2

  are the charge values and r is the distance that separates them. Electric fields are only one example of fields.

  OTHER TYPES OF FIELDS

  Gravity is another field. The gravitational force is proportional to the product of the masses of the two objects involved and is always attractive. (There is no such thing as negative mass.) The gravitational field is much weaker than the electric field, so the gravitational force is only felt when the mass of one or both of the objects is very large. Therefore, our attraction to the earth is big, while our attraction to other objects like furniture is exceedingly small.

  Another example of a field is the stress field that occurs when elastic objects are stretched or compressed. For an example, refer to Figure 2.2 . Two balls are connected by a spring. When the spring is stretched, it will exert an attractive force on the balls and try to pull them together. When the spring is compressed, it will exert a repulsive force on the balls and try to push them apart. Now imagine that you stretch the spring and then quickly release the two balls. An oscillating motion occurs. The balls move close together, then far apart and continue back and forth. The motion does not continue forever though, because of friction. Through each cycle of oscillation, the balls lose some energy until they eventually stop moving completely. The causes of fiction are the air surrounding the balls and the internal friction of the spring. The energy lost to friction becomes heat in the air and spring. Before Einstein and his theory of relativity, most scientists thought that the electric field operated in a similar manner. During the 1800s, scientists postulated that there was a substance, called aether, which filled all of space. This aether served the purpose of the spring in the previous example. Electric fields were thought to be stresses in the aether. This theory seemed reasonable because it predicted the propagation of electromagnetic waves. The waves were just stress waves in the aether, similar to mechanical waves in springs. But Einstein showed that there was no aether. Empty space is just that—empty.*

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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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  Fields of Force

  The Development of a World View from Faraday to Einstein.

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

    (Publisher)

  resting charge? Faraday did not see any way to answer this question, and so his unified theory of electricity and magnetism never quite succeeded.

  Though Faraday’s unified theory was imperfect, it served as a guide to his further experiments, and he found the different parts of it very worthy of experimental tests. For instance, he tried again to see whether a vibrating wire would have electric effects, in this case affecting a galvanometer; but there was no positive result.23 He also developed some parts of his theory and tested them experimentally. One aspect of his unified theory was that conduction and insulation were not essentially different, but just two extremes of the same process:24

  I look upon the first effect of an excited body upon neighbouring matters to be the production of a polarized state of their particles, which constitutes induction; and this arises from its action upon the particles in immediate contact with it, which again act upon these contiguous to it, and thus the forces are transferred to a distance. If induction remains undiminished, then perfect insulation is the consequence, and the higher is the intensity which may be given to the acting forces. If, on the contrary, the contiguous particles, upon acquiring the polarized state, have the power to communicate their forces, then conduction occurs, and the tension is lowered, the conduction being a distinct act of discharge between neighbouring particles. The lower state of tension at which this discharge between the particles of a body takes place, the better conductor is that body. In this view insulators are those whose particles cannot be permanently polarized. If I be right in my view of induction, then I consider the reduction of these two effects (which have been so long held distinct) to an action of contiguous particles obedient to one common law, as a very important result.

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  The Special Theory of Relativity

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

    (Publisher)

  D between successive atoms in the lattice, so that, in the last analysis, the size of such a crystal containing a specified number of atomic steps in any given direction is determined in this way.

  Lorentz assumed that the electrical forces were in essence states of stress and strain in the ether. From Maxwell’s equations (assumed to hold in the reference frame in which the ether was at rest) it was possible to calculate the electromagnetic field surrounding a charged particle. For a particle at rest in the ether, it followed that this field was derivable from a potential, , which was a spherically symmetric function of the distance R from the charge, i.e., (where q is the charge of the particle). When a similar calculation was done for a charge moving with a velocity v through the ether, it was found that the force field was no longer spherically symmetric. Rather its symmetry became that of an ellipse of revolution, having unchanged diameters in the directions perpendicular to the velocity, but shortened in the direction of motion in the ratio This shortening is evidently an effect of the movement of the electron through the ether.

  Because the electrical potential due to all the atoms of the crystal is just the sum of the potentials due to each particle out of which it is constituted, it follows that the whole pattern of equipotentials is contracted in the direction of motion and left unaltered in a perpendicular direction, in just the same way as happens with the field of a single electron. Now the equilibrium positions of the atoms are at points of minimum potential (where the net force on them cancels out). It follows then that when the pattern of equipotentials is contracted in the direction of motion, there will be a corresponding contraction of the whole bar, in the same direction, so that it will be shortened in the ratio As a result, a measuring rod of length l0 at rest will, when moving with a velocity v

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  The Big Ideas in Physics and How to Teach Them

  Teaching Physics 11–18

  • Ben Rogers(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  While philosophers developed the concept of electricity, showmen quickly realised the potential for drama: the shocks, the sparks, the ‘electrickery’. Many of the philosophers adopted the showmen’s circus style, entertaining friends and society with electric kisses, dangling boys and electrocuting turkeys for thanksgiving.

  Then came Galvani’s twitching frogs’ legs and animal electricity. Galvani’s nephew toured Europe, making the recently executed twitch and open their eyes. The idea that electricity was linked to life was used by radicals in the early 19th century to sermonise against God and the natural order.

  Then there were the quacks and medical charlatans with their electropathic belts and Pulvermacher’s Galvanic bath chains. So, it is a relief that the word electricity has fallen into disuse in modern physics, fit only as the title for courses. It is not a word to be used carelessly.

  The next three words – charge, current and potential difference – benefit from clear explanations, but explanations are not how these concepts are learnt. They are only really understood by answering as many ‘end-of-the-chapter’ questions as possible. It is the exemplars we have learnt that make us physicists.

  Electric charge

  Charge is the most fundamental, and the most slippery, of the electrical terms. It is defined as follows: “Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field” (Wikipedia 2017).

  The definition alone is hopeless.

  In physics, the word charge (Figure 1.13) is used in at least three different ways. First, and most important, charge is used as an uncountable noun – physicists often talk about charge as though it were an amount of a substance, like water or plasticine, not separated into separate droplets or chunks.

  This idea developed because physicists initially understood electricity as a flow of charge, imagining water flowing in a pipe. This uncountable use of charge is important, because it allows us to use and understand current, voltage, electric fields and the conservation of charge.

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  Electrical Engineering Fundamentals

  • S. Bobby Rauf(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 2 . For now, note that Ohm’s law is stated, mathematically, in the form of Eq. 1.41. In other words, according to Ohm’s law, electromotive force is equal to the product of current and resistance.

  E l e c t r o m o t i v e F o r c e

  , V = I ⋅ R = (

  C u r r e n t

  ) × (

  R e s i s t a n c e

  )

  (1.41)

  The circuit shown in Figure 1.26b represents a basic electromagnetic circuit. This circuit consists of a toroid or donut-shaped core – typically constructed out of iron. In this magnetic circuit, a conductor, or wire, is wrapped in four turns around the left side of the toroid core. When current is passed through wound conductor, magnetic field is established in the core as represented by the dashed circular line, with an arrow pointing in clockwise direction. This magnetic field is referred to as magnetic flux, ф . Magnetic flux is measured in weber. The unit weber is named for the German physicist Wilhelm Eduard Weber (1804–1891). In the magnetic realm, the flux serves as a counterpart to the current, I , from the electrical realm. Just like the electromotive force, EMF , or voltage, drives the current through the resistor, R , the magnetomotive force (MMF ), F , drives the magnetic flux, ф, through the toroid magnetic core. Magnetomotive force is measured in ampere-turns. In electrical systems, load is represented by the resistor R . In the magnetic circuit, the flow of magnetic flux is opposed by reluctance R . Just as Ohm’s law, represented by Eq. 1.41, governs the relationship between electromotive force (voltage), current, and resistance in the electrical realm, Eq. 1.42 represents the relationship between the magnetomotive force, F , the magnetic flux, ф, and the reluctance R

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  The Special Theory of Relativity

  • David Bohm(Author)
  • 2015(Publication Date)
  • Routledge

    (Publisher)

  It is also necessary to define the force F in such a way that it will express the same kind of relationship, independent of the speed of the reference frame. Now, this cannot actually be done until we have some more specific expressions for the force, such as that due to an electromagnetic field, to gravitation, or to other forces (e.g., those arising in nuclear interactions). In this work we shall in fact discuss only the electromagnetic forces, showing in detail that they do lead to invariant relationships for the equations of motion. It may be stated, however, that all forces with properties that are known can be expressed in such a way as to lead to similarly invariant equations of motion, but the proof of the statement is beyond the scope of the present work. 1 The force on a body of charge q under an electric field and a magnetic field is Noting that, we obtain the well-known Lorentz equations of motion for such a body: For our purposes these can more conveniently be expressed in differential form with d x / dt = v, when d x is the vector for the distance moved by the body in the time interval dt. The above laws were first observed to hold in frames of reference which are such that the velocity v of the electron is small compared with c. However, we are now investigating the conditions under which these laws will hold, independent of the speed of the frame of reference. In other words, if (21–7) and (21–8) hold in some frame A, we wish to find out how the quantities and, as observed in another frame B, must be related to and in order that the equations in frame B will have the same form, when expressed in terms of the new variables. We now express d p ′ and dE ′ in terms of d p and dE by the Lorentz transformations (20–7) and (20–8) and express d x ′ and dt ′ in terms of d x and dt by the similar transformation (15–12). In doing this we take the differentials of the corresponding equations, noting that V and are constants

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