8 Key excerpts on "Electric Field Strength"

• 

  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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  eBook - ePub

  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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  eBook - ePub

  Fundamental Electrical and Electronic Principles

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

    (Publisher)

  Fig. 3.4 .

  Fig. 3.4

  Note that the electric field will exist in all of the space surrounding the two plates, but the uniform section exists only in the space between them. Some non-uniformity is shown by the curved lines at the edges (fringing effect). At this stage we are concerned only with the uniform field between the plates. If a positively charged particle was placed between the plates it would experience a force that would cause it to move from the positive to the negative plate. The value of force acting on the particle depends upon what is known as the Electric Field Strength.

  3.3 Electric Field Strength (E) This is defined as the force per unit charge exerted on a test charge placed inside the electric field. (An outdated name for this property is ‘electric force’).

  3.4 Electric Flux (ψ) and Flux Density (D)

  In the SI system one ‘line’ of flux is assumed to radiate from the surface of a positive charge of one coulomb and terminate at the surface of a negative charge of one coulomb. Hence the electric flux has the same numerical value as the charge that produces it. Therefore the coulomb is used as the unit of electric flux. In addition, the Greek letter psi is usually replaced by the symbol for charge, namely Q.

  The electric flux density D is defined as the amount of flux per square metre of the electric field. This area is measured at right angles to the lines of force. This gives the following equation

  Worked Example 3.1 Q        Two parallel plates of dimensions 30 mm by 20 mm are oppositely charged to a value of 50 mC. Calculate the density of the electric field existing between them. A

  Q = 50 × 10−3 C; A = 30 × 20 × 10−6 m2

  Worked Example 3.2 Q       Two parallel metal plates, each having a csa of 400 mm2

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  eBook - ePub

  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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  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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  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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  Radiation Detection

  Concepts, Methods, and Devices

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

    (Publisher)

  potential, which is defined as the potential energy per unit charge,

  V = U Q ′ = 1 4 π ϵ o ∑ i = 1 n Q i r i ,	(8.16)

  and is expressed in units of volts (or joules per coulomb). Note that the potential is no longer dependent upon the “test” charge Q′ .3 The force exerted upon Q′ may also be expressed in terms of the electric field, produced by one or more point charges, in which

  F =

  Q ′

  E

  . Substitution of

  q ′

  E

  into Eq. (8.13 ) and division by Q′ gives the potential difference between two points within the electric field. Hence, the potential difference between arbitrary locations a and b is

  V a b = Δ V = ∫ a b E ⋅ d l = ∫ a b E cos ⁡ θ d l .	(8.17)

  In summary, Eq. (8.17 ) is the voltage that an experimenter would measure between two points (a and b) within an electric field. The work done on a unit test charge moving from some point a to another point b in the electric field is Q′ V

  ab

  .

  8.3Capacitance

  Consider the arrangement depicted in Fig. 8.6 . Two conductive plates, separated by a distance d, have equal, but opposite, charges. An electric field is produced between the plates by the charges on the plates. The positively charged plate (or terminal) has a voltage V1 and the negatively charged plate has a voltage V2 . The capacitance of the two plates is defined as the ratio of the charge magnitude on either plate to the magnitude of the potential difference between the plates,

  C = | Q Δ V | .	(8.18)

  If ΔV is taken as the applied voltage V between the electrodes, then the above definition gives the important relation

  C V = Q	(8.19)

  The SI unit for capacitance is the farad (one coulomb per volt). The reader should understand that the charge stored in a capacitor has a summed positive charge on one terminal and an equal summed negative charge stored on the opposite terminal; hence, a capacitor with stored charge Q actually has +Q on one terminal and −Q

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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)

  c , which turns out to be the same as the velocity of light.

  THE VELOCITY OF LIGHT, AN ELECTROMAGNETIC CONSTANT

  The important difficulty in fixing units of current is how to fix a unit which is consistent with both electrical and magnetic aspects of current. It is easy in principle to fix a unit of charge or a unit of magnetization. A unit of charge can be defined as the amount of charge on a small body which will exert a unit amount of force (measured mechanically) upon a similarly charged body a unit distance away. Likewise, a unit magnetic pole can be defined by its force effects a unit distance away. The unit of current can be based on either the magnetic or electrostatic units. For instance, consider a circuit in the shape of a circle, enclosing a unit area. If a steady current flows in the circuit, it will exert a constant magnetic force. We can say that the current is of unit strength if its magnetic force on a distant magnet is the same as that which would be produced by a magnet with poles of unit strength a unit distance apart. Here we assume that the magnet would be oriented perpendicularly to the plane of the circle. We might also define a unit of charge as the quantity of charge which passes a point of the circuit in a second, but this unit of charge, defined by electromagnetic considerations, might not agree with the unit defined above, on the basis of static electricity. What is the relation between these two units of charge? Or, to put the question another way: How many units of charge, defined statically, will pass each second by a point of a unit current, defined electromagnetically?

  The question can only be answered by experiment; it is not a question of definition but fact. The question of fact is to find what quantity of charge per second produces what strength of magnetic field. The problem of how to define units arises because we want an expression of the ratio between electrical and magnetic effects.

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