Physics
Electric Field Strength
Electric field strength is a measure of the force experienced by a unit positive charge at a given point in space. It is a vector quantity, meaning it has both magnitude and direction. The electric field strength is determined by the distribution of charges in the vicinity and is a fundamental concept in understanding the behavior of electrically charged particles.
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10 Key excerpts on "Electric Field Strength"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Definition of the Electric Field The electric field E B that exists at a point is the electrostatic force F B experienced by a small test charge* q 0 placed at that point divided by the charge itself: E B 5 F B q 0 (18.2) The electric field is a vector, and its direction is the same as the direction of the force F B on a positive test charge. SI Unit of Electric Field: newton per coulomb (N/C) Equation 18.2 indicates that the unit for the electric field is that of force divided by charge, which is a newton/coulomb (N/C) in SI units. It is the surrounding charges that create an electric field at a given point. Any pos- itive or negative charge placed at the point interacts with the field and, as a result, experi- ences a force, as the next example indicates. *As long as the test charge is small enough that it does not disturb the surrounding charges, it may be either positive or negative. Compared to a positive test charge, a negative test charge of the same magnitude experiences a force of the same magnitude that points in the opposite direction. However, the same electric field is given by Equation 18.2, in which F B is replaced by 2 F B and q 0 is replaced by 2q 0 . EXAMPLE 7 | An Electric Field Leads to a Force In Figure 18.15 the charges on the two metal spheres and the ebonite rod create an electric field E B at the spot indicated. This field has a magnitude of 2.0 N/C and is directed as in the drawing. Determine the force on a charge placed at that spot, if the charge has a value of (a) q 0 5 118 3 10 28 C and (b) q 0 5 224 3 10 28 C. Reasoning The electric field at a given spot can exert a variety of forces, depending on the magnitude and sign of the charge placed there. The charge is assumed to be small enough that it does not alter the locations of the surrounding charges that create the field.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
DEFINITION OF THE ELECTRIC FIELD The electric field E → that exists at a point is the electrostatic force F → experienced by a small test charge* q 0 placed at that point divided by the charge itself: E → = F → __ q 0 (18.2) The electric field is a vector, and its direction is the same as the direction of the force F → on a positive test charge. SI Unit of Electric Field: newton per coulomb (N/C) Equation 18.2 indicates that the unit for the electric field is that of force divided by charge, which is a newton/coulomb (N/C) in SI units. It is the surrounding charges that create an electric field at a given point. Any positive or negative charge placed at the point interacts with the field and, as a result, experiences a force, as the next example indicates. *As long as the test charge is small enough that it does not disturb the surrounding charges, it may be either positive or negative. Compared to a positive test charge, a negative test charge of the same magni- tude experiences a force of the same magnitude that points in the opposite direction. However, the same electric field is given by Equation 18.2, in which F → is replaced by − F → and q 0 is replaced by −q 0 . EX AMPLE 7 An Electric Field Leads to a Force In Figure 18.16 the charges on the two metal spheres and the ebonite rod create an electric field E → at the spot indicated. This field has a magnitude of 2.0 N/C and is directed as in the drawing. Determine the force on a charge placed at that spot, if the charge has a value of (a) q 0 = +18 × 10 −8 C and (b) q 0 = ‒24 × 10 −8 C. Reasoning The electric field at a given spot can exert a vari- ety of forces, depending on the magnitude and sign of the charge placed there. The charge is assumed to be small enough that it does not alter the locations of the surrounding charges that create the field.
eBook - PDF- Y K Lim(Author)
- 1986(Publication Date)
- WSPC(Publisher)
Chapter I FUNDAMENTAL CONCEPTS AND EXPERIMENTAL LAWS Electrodynamics deals with the fields and radiation of moving charges. In describing the interaction between charges it is convenient, both mathematically and physically, to consider it, not as forces that act at a distance, but as the force exerted by the field set up by one charge on the other. This approach is in fact essential for charges in relative motion as electromagnetic effects are found to propagate with finite velocity. The four field vectors, Ej B, D and H, which are fundamental in Maxwell's electro-magnetic theory are introduced and discussed in this chapter in a phenomenologiaal manner. In addition, a short review is made of the experimental laws which lead to Maxwell's equations. 1.1 Electric Field Intensity E Electric field is said to exist at a point where a stationary particle experiences a force on account of its charge. The electric field intensity or Electric Field Strength E is defined as the force per unit charge acting on a small positive charge q' introduced at that point. Let F be the electric force acting on the test charge, then by definition 2 . E - lim -L . (1.1) q' + OQ' The limit q' + Q is required in order that the introduction of the test charge will not significantly Influence the source; the field can then be described independently of the presence of a test charge. The finite magnitude of the elementary charge e does not permit the limiting process to be realized even in principle. The definition applies, therefore, to macroscopic phenomena only. For microscopic processes, the field is usually defined in terms of its source, assuming that the macroscopic laws governing the field-source relationship still apply. The simplest type of electric field is one that is set up by stationary charges, the electrostatic field. We shall confine ourselves in the first instance to free space.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Our goals in this chapter are to (1) define electric field, (2) discuss how to calculate it for various arrangements of charged particles and objects, and (3) dis- cuss how an electric field can affect a charged particle (as in making it move). The Electric Field A lot of different fields are used in science and engineering. For example, a tem- perature field for an auditorium is the distribution of temperatures we would find by measuring the temperature at many points within the auditorium. Similarly, we could define a pressure field in a swimming pool. Such fields are examples of scalar fields because temperature and pressure are scalar quantities, having only magnitudes and not directions. In contrast, an electric field is a vector field because it is responsible for conveying the information for a force, which involves both magnitude and direc- tion. This field consists of a distribution of electric field vectors E → , one for each point in the space around a charged object. In principle, we can define E → at some point near the charged object, such as point P in Fig. 22-2a, with this proce- dure: At P, we place a particle with a small positive charge q 0 , called a test charge because we use it to test the field. (We want the charge to be small so that it does not disturb the object’s charge distribution.) We then measure the electrostatic force F → that acts on the test charge. The electric field at that point is then E → = F → q 0 (electric field). (22-1) Because the test charge is positive, the two vectors in Eq. 22-1 are in the same direction, so the direction of E → is the direction we measure for F → . The magnitude of E → at point P is F/q 0 . As shown in Fig. 22-2b, we always represent an electric field with an arrow with its tail anchored on the point where the measurement is made.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
630 CHAPTER 22 Electric Fields Our goals in this chapter are to (1) define electric field, (2) discuss how to calculate it for various arrangements of charged particles and objects, and (3) discuss how an electric field can affect a charged particle (as in making it move). The Electric Field A lot of different fields are used in science and engineering. For example, a tem- perature field for an auditorium is the distribution of temperatures we would find by measuring the temperature at many points within the auditorium. Similarly, we could define a pressure field in a swimming pool. Such fields are examples of scalar fields because temperature and pressure are scalar quantities, having only magnitudes and not directions. In contrast, an electric field is a vector field because it is responsible for conveying the information for a force, which involves both magnitude and direc- tion. This field consists of a distribution of electric field vectors E → , one for each point in the space around a charged object. In principle, we can define E → at some point near the charged object, such as point P in Fig. 22.1.2a, with this proce- dure: At P, we place a particle with a small positive charge q 0 , called a test charge because we use it to test the field. (We want the charge to be small so that it does not disturb the object’s charge distribution.) We then measure the electrostatic force F → that acts on the test charge. The electric field at that point is then E → = F → ___ q 0 (electric field). (22.1.1) Because the test charge is positive, the two vectors in Eq. 22.1.1 are in the same direction, so the direction of E → is the direction we measure for F → . The mag- nitude of E → at point P is F/q 0 . As shown in Fig. 22.1.2b, we always represent an electric field with an arrow with its tail anchored on the point where the mea- surement is made.
eBook - ePub- Michael M. Mansfield, Colm O'Sullivan(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
E is given byFrom the definition of E it follows that the SI unit of Electric Field Strength is N C−1 . Recalling that , and , we can writeso that Electric Field Strengths are commonly stated in volt per metre.For problems based on the material presented in this section visit up.ucc.ie/16/ and follow the link to the problems.16.3 Forces between point charges: Coulomb's law
The nature of the force between electric charges exercised the minds of scientists throughout the second half of the eighteenth century. By then, Newton's law of gravitation was already well established and many suspected that the force between point charges might also obey an inverse square law. The French scientist Charles‐Augustin de Coulomb (1736–1806), who is credited with inventing the torsion balance (Section 7.5 ), used such a device to determine how the force between charges depends on the distance between them.The principles of Coulomb's torsion balance are shown in Figure 16.8
eBook - PDF- M. Sibley(Author)
- 1995(Publication Date)
- Butterworth-Heinemann(Publisher)
We should note that,as E is directlyproportionalto D, it is also a vector quantity. The fieldstrengthis animportantparameterin that it introducesus to the idea of a force field. Figure 2.5(a) shows an isolated point charge at the centre IIs,D,E ljI,D,E Gaussian Gaussian sphere sphere lis IjJ lis lJI D D D D f f e f ~~E ~~f (a) (b) Fig. 2.5 Flux, flux density and Electric Field Strength in (a) a positive charge field; and (b) a negative charge field 14 Electrostatic fields 2.3 THE ELECTRIC FIELD AND Electric Field Strength As we saw in the previous section, we can write Coulomb's law as * 1 4ttr 2 Izr If we use the definition of electric flux density gives by Equation (2.4) we can write D ■12 (2.5) In Equation (2.5) we can see that the force oa the charge q 2 is directly proportiona l to the factor JD/c. This factor has units of newton per coulomb» i.e. N C~ Thtis we can regard this quantity as the force on a unit of charge . To emphasiz e this more, we introduce a new paramete r known as the Electric Field Strength , E, defined as D E = — € We can now write Coulomb' s law as F=q 2 E or, more generally» F=qE (2.6) (2.7) From this equation we can see that the force is directly dependen t on the electric field strengt h also known as the electric field intensity* We shoul d note that, as E is directly proportional to D 9 it is also a vector quantity» The field strengt h is an importan t paramete r in. that it introduces us to the idea of a force field. Figure 2.5(a) shows an isolated point charge at the centre ty,D,E éME i|; i B j <~~—*«é % i Gaussiai ■ ,^ /'sphere | « * « _ ^ ^ i E 1 D E / i ' ■ — ^ Gaussian /sphere '. + ;---<|i,D,£ *MW? m
eBook - PDFElectromagnetism for Engineers
An Introductory Course
- P. Hammond(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
14 Electromagnetism for Engineers 2.4 THE ELECTRIC FORCE IS A VECTOR QUANTITY In order to define a force acting on a body we have to know its magnitude and direction. Force is a vector quantity and the force between electric charges is no exception to this rule. When we are deaUng with two point charges by themselves then this force must act along the fine joining the charges. This is a consequence of Newton's third law that action and reaction are equal and opposite. When there are several charges we must add the forces vectorially. Consider two simple cases. In Fig. 2.2 three positive charges lie along the same Hne. The force on Q2 from left to right is given by: F= Q1Q2 Q3Q2 4neQa' Ö2 ÍQi 4πεη Va^ Ol (2.8) a b FIG. 2.2 Three charges in a line In Fig. 2.3, three equal charges lie at the corners of an equilateral triangle ABC of side a. The force on the charge Ö at A is given by the vector sum of a force (2.9) along BA and a similar force along CA. Thus the resultant force on Ö at A is F = 2 s i n 60° (2.10) perpendicular to BC. FIG. 2.3 Β a C Three equal charges at the corners of a triangle Electric Charges at Rest—I 15 2.5 Electric Field Strength Let us now take a close look at eqn. (2.8). There are two forces, which both contain Q2 and this is reasonable because we are concerned with the force on Ö2 · In the general case F = Ö 2 X function (Ö 1 ,03,04,..., Q,). We can thus take Q2 out as a common factor and this suggests another way of looking at the problem. Instead of applying the inverse square law directly we can proceed in two steps as follows. The force on Q2 is proportional to Q2, let it be written as EQ2, where Ε describes the effect of the charges Q j and at the place where Ö2 is. In the case of Fig. 2.2 ^ = Z ^ -Z % (2.11) along the line joining the charges and acting from left to right. In the case of Fig. 2.3 £ = 2 sin 60° = (2.12) perpendicular to BC. Ε has magnitude and direction and is called the Electric Field Strength.
eBook - ePub- Sivaji Chakravorti(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
1Fundamentals of Electric Field
ABSTRACT Leaving aside nuclear interactions, there are two non-contact forces that act at a distance, namely, gravitational and electric forces. Gravitational force is dominant at large distances whereas electric forces are dominant at shorter distances. The root cause of electric forces is electric charge. The effect of electric charge is spread over the entire space around it, but it falls rapidly with distance. The presence of an electric field is detected by observing the force on a charged body located within the field region. Electric field intensity is obtained by dividing the electric force by the magnitude of the test charge. To have an electric field parameter, which is independent of the charge of the test body, electric potential is introduced in the analysis, such that electric field intensity, which is a vector quantity, is the spatial derivative of electric potential, which is a scalar quantity. For a given material, electric field intensity depends on the electric flux density, which in turn depends on the amount of source charges present in the field region. For the purpose of electric field analysis, several types of charge configurations are considered, such as point, line, ring and disc charges.1.1 Introduction
When I was a student of third semester in engineering degree course, I had an unassuming yet a man of profound knowledge as our teacher who taught us electric field theory. In the very first class, he asked us a simple question: ‘Could you name just one thing which is the cause of electric field?’ Then he went on to explain the answer to that question, which is ‘Electric Charge’. It struck a chord somewhere within me, and I explored further on the effects of electric charge. From that day onwards, I was hooked to electric charge.To quote the legendary physicist, Richard Feynman, ‘Observation, reason, and experiment make up what we call the scientific method’. This is precisely true for electric field theory. Students often ask me how I discussed so many things about electric field when nobody has seen electric field. Yes, it is true that electric field cannot be directly seen. But observations on physical occurrences and related reasoning give theoretical understanding and when such understanding is validated by experimentation, then it establishes the existence of electric field.
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2022(Publication Date)
- Società Editrice Esculapio(Publisher)
Electrostatic Field and Electrostatic Potential 2.1 Introduction Electrostatic force, as defined by Coulomb’s law, is formally identical to gravitational force, as expressed by Newton’s law, with the mere substitution of the mass of the bodies with their charge. It is therefore possible to define an electrostatic field, in full analogy with respect to the gravitational field definition, as the region of the space where an electrostatic force is exerted and it is also possible to associate an electrostatic potential with each point of this region. The general properties of an electrostatic force and of a gravitational force are obviously the same. 2.2 Electrostatic field Consider a point-like particle of mass m, charged with an amount of electric charge q, which lies in an empty space, that is in a region of the space where all the other bodies are placed at a very large distance from the selected body. Bring from infinite distance another point-like body which carries a charge ′ q (usually called test-charge) into this empty space and measure the intensity and the direction of the force being exerted between the two charges q and ′ q in each point P which belongs to this space. This operation draws a map of the electrostatic force vector F = 1 4πε 0 q ′ q r 2 u r , where u r is the unit vector of a polar coordinate reference system whose origin is chosen in point O, where body m is placed. Such a map is correct only if the size of body m with respect to the distance from point P, where charge ′ q is placed, is truly negligible, because electrostatic induction causes charge displacement both inside the body and on its surface. The map is therefore exact in the whole space only if the charge ′ q has a negligible value and therefore it cannot generate any relevant displacement of charge q which modifies how it is distributed in a body.
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