Physics
Electric Force
Electric force is a fundamental force of nature that describes the attraction or repulsion between charged particles. It is responsible for the interactions between electrons and protons within atoms, as well as the behavior of electrically charged objects. The strength of the electric force is determined by the magnitude of the charges and the distance between them, as described by Coulomb's law.
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eBook - PDFThe Mechanical Universe
Mechanics and Heat, Advanced Edition
- Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein(Authors)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
The French engineer Charles Augustin Coulomb assumed that, anal-ogous to the gravitational force between two masses, the Electric Force between two charges is proportional to the product of the charges. Experimentally, he found that the Electric Force is similar to gravity in another way: the force between two charges decreases as the square of the distance between them. Summarized mathematically, the Electric Force F between two charges q f and q 2 which are separated by a distance r is known as Coulomb's law and written as (8.2) Just as G is a universal constant for gravity, K e is a universal constant for electricity. Magnetism was also identified as a fundamental force of nature. The attraction or repulsion between two magnets could be described by a force between pairs of magnetic poles. The progress of physics appeared to be a triumph of Newtonian mechanics: the forces of nature were successively reduced to attractions and repulsions between particles. The first 40 years of the nineteenth century, however, saw a growing reaction against such a division of phenomena in favor of some kind of correlation of forces. The turn inward to unification of forces was spearheaded by Oersted, Ampere, and Faraday. By the middle of the century they had succeeded in unifying two hitherto disparate forces, electricity and magnetism, into one - eiectromagnetism. The process was crowned in the theory of James Clerk Maxwell, who expressed the unification by a set of equations which interrelate electric and magnetic phenomena. Soon tensions, spring forces, friction, viscosity, chemical actions, and even light were recognized as arising fundamentally from the electromagnetic force. Based on Maxwell's success the search for a common math-ematical description, or unification, of forces had begun.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
• The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles. 18.4 Electric Field: Concept of a Field Revisited • The electrostatic force field surrounding a charged object extends out into space in all directions. • The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the distance between the two. • The electric field E is defined to be E = F q, where F is the Coulomb or electrostatic force exerted on a small positive test charge q . E has units of N/C. • The magnitude of the electric field E created by a point charge Q is 722 Chapter 18 | Electric Charge and Electric Field This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 E = k | Q | r 2 . where r is the distance from Q . The electric field E is a vector and fields due to multiple charges add like vectors. 18.5 Electric Field Lines: Multiple Charges • Drawings of electric field lines are useful visual tools. The properties of electric field lines for any charge distribution are that: • Field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges. • The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. • The strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area perpendicular to the lines. • The direction of the electric field is tangent to the field line at any point in space. • Field lines can never cross. 18.6 Electric Forces in Biology • Many molecules in living organisms, such as DNA, carry a charge. • An uneven distribution of the positive and negative charges within a polar molecule produces a dipole.
eBook - ePubElectromagnetics 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 chargeTo 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 aswhere 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,whereq1andq2are 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.*
eBook - ePub- I. S. Grant, W. R. Phillips(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
1 isIn general, the force Fj on a chargeqjdue to a number of other chargesqiisThe symbol i ≠ j under the summation signs indicates that the summation for charge i is over all the other charges j , but of course not including charge i itself. This equation can be written in another way in terms of the position vectors of the charges with respect to a fixed origin O. If the position vectors of the charges q 1 , q 2 … q i … are r1 , r2 … ri … then the vector joining charges i and j is rij = rj – ri . The total force onqjis thus(1.3)A trivial example of the application of Equation (1.3) is in working out the electrostatic forces exerted by atomic nuclei containing many protons on the electrons surrounding them. Nuclei are much smaller than atoms, and for this purpose can be regarded as point charges. Equation (1.3) then tells us that the attractive force between an electron and a nucleus containing Z protons is Z times as great as that between an electron and a single proton.It turns out that apart from the sign, the charge carried by electrons and protons is the same, and has the magnitude e = 1.602 × 10−19 coulombs* : the charge on the proton is +e , that on the electron is – e . The strength of atomic interactions is governed by the size of the electronic charge e . Although e
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
(b) Two negative charges repel each other. (c) Two positive charges repel each other. (a) + – (b) – – + + (c) Like other forces that we have encountered, the Electric Force (also sometimes called the electrostatic force) can alter the motion of an object. It can do so by contributing to the net external force Σ F that acts 478 Physics on the object. Newton’s second law, Σ F = m a, specifies the acceleration a that arises because of the net external force. Any external Electric Force that acts on an object must be included when determining the net external force to be used in the second law. THE PHYSICS OF . . . Electronic ink A new technology based on the Electric Force may revolu- tionise the way books and other printed matter are made. This technology, called electronic ink, allows letters and graphics on a page to be changed instantly, much like the symbols displayed on a computer monitor. Figure 18.4a illustrates the essential features of electronic ink. It consists of millions of clear microcapsules, each having the diameter of a human hair and filled with a dark, inky liquid. Inside each microcapsule are several dozen extremely tiny white beads that carry a slightly negative charge. The microcap- sules are sandwiched between two sheets, an opaque base layer and a transparent top layer, at which the reader looks. When a positive charge is applied to a small region of the base layer, as shown in part b of the drawing, the negatively charged white beads are drawn to it, leaving dark ink at the top layer. Thus, a viewer sees only the dark liquid. When a negative charge is applied to a region of the base layer, the negatively charged white beads are repelled from it and are forced to the top of the microcapsules; now a viewer sees a white area due to the beads.
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.
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Protons subjected to such a net force would go flying out of the nucleus. Protons stay in the nucleus because another force—known as the strong nuclear force—is attractive and holds them inside. The Strong Force EXAMPLE 23.10 ! Underlying Principles 1. Conservation of charge. The net charge in the Uni- verse is constant. Charge may transfer from one ob- ject to another, but it is not created, lost, or destroyed. 2. Electrostatic force between charged objects is (part of) one of the fundamental forces in physics. If two objects are oppositely charged, they are mutually attracted. If two objects have charges of the same sign, they are mutually repelled. (Opposites attract; likes repel.) 3. Coulomb’s law. For two charged objects that can be modeled as particles with charges q 1 and q 2 , the magnitude of the electrostatic force is given by F E 5 k 0 q 1 q 2 0 r 2 (23.3) where r is the distance between the particles. If polar coordinates are used so that the unit vector r ^ points from q 1 toward q 2 , Coulomb’s law is written in vec- tor form as F u 32 on 14 5 2k q 1 q 2 r 2 r ˆ (23.4) In this chapter, we began to study a new branch of physics—electricity. When an object has a net charge, it exerts an electrostatic force on other charged objects or on neutral objects. The electrostatic force between particles is similar to gravity because both forces are inversely proportional to the square of the distance between the particles. However, unlike gravity, the electrostatic force can be either attractive or repulsive. Unless otherwise noted, all content on this page is © Cengage Learning. Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 4. E As part of a demonstration, a physics professor rubs wool against a plastic disk about the size and mass of a small dinner plate. Afterward, the disk has a charge of about 275 mC. Esti- mate the fractional increase in the number of electrons.
eBook - ePub- Sivaji Chakravorti(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
It is the law that describes the electrostatic interaction between electrically charged particles. It was published by the French physicist Charles Augustin de Coulomb in 1785. He determined the magnitude of the Electric Force between two point charges using a torsion balance to study the attraction and repulsion forces of charged particles. The interaction between charged particles is a non-contact force that acts over some distance of separation. There are always two charges and a separation distance between them as the three critical variables that influence the strength of the electrostatic interaction. The unit of the electrostatic force, like all forces, is Newton. Being a force, the strength of the electrostatic interaction is a vector quantity that has both magnitude and direction.According to the statement of Coulomb’s law (1) the magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of point charges and inversely proportional to the square of the separation distance between the point charges and (2) the electrostatic force of interaction acts along the straight line joining the two point charges. If the two point charges are of same polarity, the electrostatic force between them is repulsive; if they are of opposite polarity, the force between them is attractive.FIGURE 1.3 Electrostatic forces of interaction between two point charges.It should be noted here that two conditions are to be fulfilled for the validity of Coulomb’s law: (1) the charges involved must be point charges and (2) the charges should be stationary with respect to each other.Mathematically, the force between two point charges, as shown in Figure 1.3 , could be written as follows:where:=F →2 1±Q 2⋅Q 14 πε 0|r →2 1| 2andu ˆr 2 1=F →1 2Q 1⋅ ±Q 24 πε 0|r →1 2| 2sothatu ˆr 1 2= -F →2 1F →1 2 ( 1.1 )- ε0 is permittivity of free space (≈8.854187 × 10–12
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 - 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.
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