Physics
Induced Surface Charge
Induced surface charge refers to the redistribution of electric charge on a conductor's surface when it is brought near a charged object. This redistribution occurs due to the influence of the external electric field, leading to the separation of positive and negative charges on the surface. The induced surface charge creates an electric field that opposes the external field, resulting in electrostatic equilibrium.
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7 Key excerpts on "Induced Surface Charge"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
564 CHAPTER 18 Electric Forces and Electric Fields r Spherical Gaussian surface Electric field lines +q FIGURE 18.32 A positive point charge is located at the center of an imaginary spherical surface of radius r. Such a surface is one example of a Gaussian surface. Here the electric field is perpendicular to the surface and has the same magnitude everywhere on it. the charge on the interior surface in this answer is positive, and field lines must end on negative charges. Thus, this answer is incorrect. Answer (d) is correct. Since the field lines emanating from the suspended positive charge +q terminate only on nega- tive charges and do not penetrate the metal, there must be an induced negative charge on the interior surface. Furthermore, the lines begin and end on equal amounts of charge, so the magnitude of the total charge induced on the interior surface is the same as the magnitude of the suspended charge. Thus, the charge induced on the interior surface is ‒q. We know that the total net charge on the metallic conductor must remain at zero. Therefore, if a charge ‒q is induced on the interior surface, there must also be a charge of +q induced on the exterior sur- face, because excess charge cannot remain inside of the solid metal at equilibrium. 18.9 Gauss’ Law Section 18.6 discusses how a point charge creates an electric field in the space around the charge. There are also many situations in which an electric field is produced by charges that are spread out over a region, rather than by a single point charge. Such an extended collection of charges is called a charge distribution. For example, the electric field within the parallel plate capacitor in Figure 18.21 is produced by positive charges spread uni- formly over one plate and an equal number of negative charges spread over the other plate. As we will see, Gauss’ law describes the relationship between a charge distribution and the electric field it produces.
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2022(Publication Date)
- Società Editrice Esculapio(Publisher)
However, the conductor restores its electrostatic equilibrium in a very short time by forcing the excess charge to distribute on its surface. In fact electrostatic equilibrium occurs if the electrostatic field in the conductor is null. Hence, being E = 0, Gauss’s law applied to any surface inside the conductor provides EidA u n Gauss surface ∫ = q in ε 0 = 0 ⇒ q in = 0 and, since such a Gauss surface can be as large as the outer conduc- tor surface, no net amount of charge can exist in the conductor vol- ume. Therefore, any excess charge must be distributed on its outer surface. In electrostatic equilibrium the electrostatic potential cannot be different in different E=0 Gauss surface + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 57 5 points of a conductor. In fact, considering a generic path γ which connects any two points A and B of a conductor in electrostatic equilibrium, the difference in electrostatic potential is given by ΔV BA = − Eid r = 0 Aγ B ∫ because the electrostatic field is anywhere null in it. Then all the points which belong to a conductor share the same potential, which depends on the amount of excess charge, and, in particular, the conductor surface is equipotential. The excess charge is distributed on the equipotential surface of a conductor. By con- necting two or more conductors, they become electrically a single conductor and then the excess charge must be rearranged in order to restore electrostatic equilibrium. As a conse- quence, the assembled conductor, as a whole, must present an equipotential external surface and the excess charge must redistribute on its external surface accordingly. 5.4 Coulomb’s Theorem Consider a portion of a charged conductor: all the excess charge is distributed on its surface which is equipotential thus, because of the properties of equipotential surfaces out- lined in paragraph 2.12, the generated electrostatic field is normal to the conductor surface in any of its points.
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)
Even so, having the ability to detect small electric fields even a few metres away allows the shark to locate food that might be hiding beneath sand, for example. 504 Physics CONCEPT SUMMARY 18.1 Define electric charge. There are two kinds of electric charge: positive and negative. The SI unit of electric charge is the coulomb (C). The magnitude of the charge on an electron or a proton is e = 1.60 × 10 −19 C. Since the symbol e denotes a magnitude, it has no algebraic sign. Thus, the electron carries a charge of −e, and the proton carries a charge of +e. The charge on any object, whether positive or negative, is quantised, in the sense that the charge consists of an integer number of protons or electrons. 18.2 Describe the electric force between charged particles. The law of conservation of electric charge states that the net electric charge of an isolated system remains constant during any process. Like charges repel and unlike charges attract each other. 18.3 Distinguish between conductors and insulators. An electrical conductor is a material, such as copper, that conducts electric charge readily. An electrical insulator is a material, such as rubber, that conducts electric charge poorly. 18.4 Explain charging by contact and charging by induction. Charging by contact is the process of giving one object a net electric charge by placing it in contact with an object that is already charged. Charging by induction is the process of giving an object a net electric charge without touching it to a charged object. 18.5 Use Coulomb’s law to calculate the force on a point charge due to other point charges. A point charge is a charge that occupies so little space that it can be regarded as a mathematical point. Coulomb’s law gives the magnitude F of the electric force that two point charges q 1 and q 2 exert on each other, according to equation 18.1, where |q 1 | and |q 2 | are the magnitudes of the charges and have no algebraic sign.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Induced charges appear on the inner and outer surfaces of the conductor. The electric field within the conductor itself is zero. 510 CHAPTER 18 Electric Forces and Electric Fields 18.9 Gauss’ Law Section 18.6 discusses how a point charge creates an electric field in the space around the charge. There are also many situations in which an electric field is produced by charges that are spread out over a region, rather than by a single point charge. Such an extended collection of charges is called a charge distribution. For example, the electric field within the parallel plate capacitor in Figure 18.21 is produced by positive charges spread uniformly over one plate and an equal number of negative charges spread over the other plate. As we will see, Gauss’ law describes the relationship between a charge distribution and the electric field it produces. This law was formulated by the German mathematician and physicist Carl Friedrich Gauss (1777–1855). In presenting Gauss’ law, it will be necessary to introduce a new idea called electric flux. The idea of flux involves both the electric field and the surface through which it passes. By bring- ing together the electric field and the surface through which it passes, we will be able to define electric flux and then present Gauss’ law. We begin by developing a version of Gauss’ law that applies only to a point charge, which we assume to be positive. The electric field lines for a positive point charge radiate outward in all directions from the charge, as Figure 18.22b indicates. The magnitude E of the electric field at a distance r from the charge is E = kq/r 2 , according to Equation 18.3, in which we have replaced the symbol |q| with the symbol q since we are assuming that the charge is positive. As mentioned in Section 18.5, the constant k can be expressed as k = 1/(4 0 ), where 0 is the permittivity of free space. With this substitution, the magnitude of the electric field becomes E = q/(4 0 r 2 ).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Therefore, if a charge 2q is induced on the interior surface, there must also be a charge of 1q induced on the exterior surface, because excess charge cannot remain inside of the solid metal at equilibrium. Related Homework: Problem 65 18.9 | Gauss’ Law Section 18.6 discusses how a point charge creates an electric field in the space around the charge. There are also many situations in which an electric field is produced by charges that are spread out over a region, rather than by a single point charge. Such an extended col- lection of charges is called a charge distribution. For example, the electric field within the parallel plate capacitor in Figure 18.21 is produced by positive charges spread uniformly over one plate and an equal number of negative charges spread over the other plate. As we will see, Gauss’ law describes the relationship between a charge distribution and the elec- tric field it produces. This law was formulated by the German mathematician and physicist Carl Friedrich Gauss (1777–1855). In presenting Gauss’ law, it will be necessary to introduce a new idea called electric flux. The idea of flux involves both the electric field and the surface through which it passes. By bringing together the electric field and the surface through which it passes, we will be able to define electric flux and then present Gauss’ law. We begin by developing a version of Gauss’ law that applies only to a point charge, which we assume to be positive. The electric field lines for a positive point charge radiate outward in all directions from the charge, as Figure 18.22b indicates. The mag- nitude E of the electric field at a distance r from the charge is E 5 kq/r 2 , according to Equation 18.3, in which we have replaced the symbol uqu with the symbol q since we are assuming that the charge is positive. As mentioned in Section 18.5, the constant k can be expressed as k 5 1/(4pP 0 ), where P 0 is the permittivity of free space.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Charging by induc- tion is the process of giving an object a net electric charge without touching it to a charged object. 18.5 Coulomb’s Law A point charge is a charge that occupies so little space that it can be regarded as a mathematical point. Coulomb’s law gives the magnitude F of the electric force that two point charges q 1 and q 2 exert on each other, according to Equation 18.1, where uq 1 u and uq 2 u are the mag- nitudes of the charges and have no algebraic sign. The term k is a constant and has the value k 5 8.99 3 10 9 N ? m 2 /C 2 . The force specified by Equation 18.1 acts along the line between the two charges. The permittivity of free space P 0 is defined by the relation k 5 1 4 p P 0 18.6 The Electric Field The electric field E B at a given spot is a vector and is the electrostatic force F B experienced by a very small test charge q 0 placed at that spot divided by the charge itself, as given by Equation 18.2. The direction of the electric field is the same as the direction of the force on a positive test charge. The SI unit for the electric field is the newton per coulomb (N/C). The source of the elec- tric field at any spot is the collection of charged objects surrounding that spot. The magnitude of the electric field created by a point charge q is given by Equation 18.3, where uqu is the magnitude of the charge and has no algebraic sign and r is the distance from the charge. The electric field E B points away from a positive charge and toward a negative charge. For a parallel plate capacitor that has a charge per unit area of s on each plate, the magnitude of the electric field between the plates is given by Equation 18.4. 18.7 Electric Field Lines Electric field lines are lines that can be thought of as a “map,” insofar as the lines provide information about the direction and strength of the electric field. The lines are directed away from positive charges and toward negative charges.
- Syed Tofail(Author)
- 2011(Publication Date)
- Royal Society of Chemistry(Publisher)
1 The real charge may appear due to the charge carrier injection ( e.g. from an attached electrode, an electric or corona discharge, electron beam irradiation, etc. ) to the dielectric material, followed by the capturing of the carriers in surface or volume traps of various origin. 27 Surface Charge Measurements on Biomaterials in Dry and Wet Conditions There are many ways to form electrical charges in dielectric materials, for example, by applying a strong electric field across the material which may cause injection of charge carriers or polarization, or both, by electron beam irra-diation and corona charging on the surface. The corona charging of bioma-terials is discussed in detail in Chapter 4. Some charges can be produced by heating of dielectric material in the strong electric and/or magnetic field and then cooling slowly to an ambient temperature. Some dielectric materials can form electric charges simply by a thermal heating without an electric and magnetic field or by applying mechanical pressure. 2 A common polarization method is contact poling, which is performed by applying an electrical field ( E ) for time, t , at temperature, T . In the case of ferroelectric materials, this temperature can be below or above the Curie temperature T c, at which a ferro-to-paraelectric transition takes place. As, for ferroelectric materials, the polarizability is highest at a temperature just below T c , the poling is most effective if the sample is heated just above T c and then is cooled back down to room temperature while an electric field is still applied (assuming T c is above the room temperature). 3 The stored charge can be measured directly, for example, by TSDC as dis-cussed in Section 3.3. Non-contact and non-destructive methods based on the measurement of the electric fields created by the charges are also applicable. Such measurements provide the way to detect the density of charge at the surface and in the bulk volume.
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