Figure 15-1 Simplistic model of atoms The so-called solar system model of (a) a hydrogen atom and (b) a beryllium atom views the electrons (negatively charged) as orbiting the nucleus (positively charged), analogously to the planets orbiting the Sun. The electronic structure of atoms is actually much more complicated than this.
Figure 15-2 The charge–force law, or law of charges (a) Like charges repel. (b) Unlike charges attract.
Table 15-1 Sub-atomic Particles and Their Electric Charge
Figure 15-3 Conductors, semiconductors, and insulators A comparison of the relative magnitudes of the electrical conductivities of various materials (not drawn to scale).
Figure 15-4 The electroscope An electroscope can be used to determine whether an object is electrically charged. When a charged object is brought near the bulb, the leaf moves away from the metal piece.
Figure 15-5 Charging by conduction (a) The electroscope is initially neutral (but the charges are separated), as a charged rod touches the bulb. (b) Charge is transferred to the electroscope. (c) When a rod of the same charge is brought near the bulb, the leaf moves farther apart. (d) When an oppositely charged rod is brought nearby, the leaf collapses.
Figure 15-6 Charging by induction (a) Touching the bulb with a finger provides a path to ground for charge transfer. The symbol e - stands for “electron.” (b) When the finger is removed, the electroscope has a net positive charge, opposite that of the rod.
Figure 15-7 Polarization (a) When the balloons are charged by friction and placed in contact with the wall, the wall is polarized. That is, an opposite charge is induced on the wall’s surface, to which the balloons then stick by the force of electrostatic attraction. The electrons on the balloon do not leave the balloon because its material (rubber) is a poor conductor. (b) Some molecules, such as those of water, are polar by nature; that is, they have permanently separated regions of positive and negative charge. But even some molecules that are not normally dipolar can be polarized temporarily by the presence of a nearby charged object. The electric force induces a separation of charge and, consequently, temporary molecular dipoles.
Figure 15-8 Coulomb’s law a) The mutual electrostatic forces on two point charges are equal and opposite. (b) For a configuration of two or more point charges, the force on a particular charge is the vector sum of the forces on it due to all the other charges. (Note: In each of these situations, all of the charges are of the same sign. How can we tell that this is true? Can you tell their sign? What is the direction of the force on q 2 due to q 3 ?)
Figure 15-10 Coulomb’s law and electrostatic forces
Figure 15-11 Electric field direction a) The mutual electrostatic forces on two point charges are equal and opposite. (b) For a configuration of two or more point charges, the force on a particular charge is the vector sum of the forces on it due to all the other charges. (Note: In each of these situations, all of the charges are of the same sign. How can we tell that this is true? Can you tell their sign? What is the direction of the force on q 2 due to q 3 ?)
Figure 15-12 Electric field (a) The electric field points away from a positive point charge, in the direction a force would be exerted on a small positive test charge. The field’s magnitude (the lengths of the vectors) decreases as the distance from the charge increases, reflecting the inverse-square distance relationship characteristic of the field produced by a point charge. (b) In this simple case, the vectors are easily connected to give the electric field line pattern due to a positive point charge.
Learn by Drawing 15-1 Using the Superposition Principle to Determine the Electric Field Direction To estimate the direction of the electric field at any point P, draw the individual electric fields vectors and add them, taking into account the relative field magnitudes if you can. In this situation, E 1 is much smaller than E 2 because of both distance and charge factors. Can you explain why the vector representing E 2, if drawn accurately, would be about eight times as long as that of E 1 ? The final step is to complete the vector addition.
Learn by Drawing 15-2 Sketching Electric Lines of Force How many lines should be drawn for - 1½ q, and what should their direction be?
Figure 15-15 Mapping the electric field due to a dipole (a) The construction of one electric field line from a dipole is shown. The electric field is the vector sum of the two fields produced by the two ends of the dipole. (See Example 15.8 for details.) (b) The full electric dipole field is determined by following the procedure in part (a) at other locations near the dipole.
Figure 15-16 Electric field due to very large parallel plates (a) Above a positively charged plate, the net electric field points upward. Here, the horizontal components of the electric fields from various locations on the plate cancel out. Below the plate, E points downward. (b) For a negatively charged plate, the electric field directions (shown on both sides of the plate) are reversed. (c) Superimposing the fields from both plates results in cancellation outside the plates and an approximately uniform field between them.
Insight 15-1 Lightning and Lightning Rods Cloud polarization induces a charge on the Earth’s surface.
Insight 15-2 Electric Fields in Law Enforcement and Nature: Stun Guns and Electric Fish The Taser stun gun A sketch of the electric field between the electrodes. (The charges change sign periodically, producing an oscillating electric field.)
Insight 15-2 Electric Fields in Law Enforcement and Nature: Stun Guns and Electric Fish Electric Fish (left) At an instant in time, the approximate electric field produced by the elephant nose fish’s electric organ, located near its tail. (The field actually oscillates.) (right) At an instant in time, the approximate electric field produced by an electric eel. The electric organ in the eel is capable of producing fields that can kill and stun as well as locate and communicate.
Figure 15-17 Electric fields Electric fields for (a) like point charges and (b) unequal like point charges.
Figure 15-18 Electric fields and conductors (a) Under static conditions, the electric field is zero inside a conductor. Any excess charge resides on the conductor’s surface. For an irregularly shaped conductor, the excess charge accumulates in the regions of highest curvature (the sharpest points), as shown. The electric field near the surface is perpendicular to that surface and strongest where the charge is densest. (b) Under static conditions, the electric field must not have a component tangential to the conductor’s surface.
Figure 15-19 Concentration of charge on a curved surface (a) On a flat surface, the repulsive forces between excess charges are parallel to the surface and tend to push the charges apart. On a sharply curved surface, in contrast, these forces are directed at an angle to the surface. Their components parallel to the surface are smaller, allowing charge to concentrate in such areas. (b) Taken to the extreme, a sharply pointed metallic needle has a dense concentration of charge at the tip. This produces a large electric field in the region above the tip, which is the principle of the lightning rod.
Figure 15-21 Various Gaussian surfaces and lines of force (a) Surrounding a single positive point charge, (b) surrounding a single negative point charge, and (c) surrounding a larger negative point charge. (d) Four different surfaces surrounding various parts of an electric dipole.
Figure 15-22 Water analogy to Gauss’s law A net outward flow of water indicates a source of water inside closed surface 1. A net inward flow of water indicates a water drain inside closed surface 2.
Figure 15-23 Gauss’s law: Excess charge on a conductor
Figure 15-24 Hydrogen atom See Exercises 36 and 37.
Figure 15-25 Charge triangle See Exercises 38, 59, and 60.
Figure 15-26 Charge rectangle See Exercises 39, 61, and 65.
Figure 15-27 Repelling pith balls See Exercise 40.
Figure 15-28 A point charge inside a thick metal spherical shell See Exercise 47.
Figure 15-29 Electric dipole field See Exercise 66.
Figure 15-30 Safe inside a car? See Exercise 70.