# Vern J. Ostdiek Donald J. Bord Chapter 7 Electricity (Section 2)

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Vern J. Ostdiek Donald J. Bord Chapter 7 Electricity (Section 2)

7.2 Electric Force and Coulomb’s Law The original amber effect illustrates that electric charges can exert forces. You may have noticed hair being pulled toward a charged comb or “static cling” between items of clothes removed from a dryer. These are among the most common situations illustrating this effect—two objects with opposite charges attracting each other.

7.2 Electric Force and Coulomb’s Law The negatively charged comb exerts an attractive force on the positively charged hair. In addition, two objects with the same kind of charge (both positive or both negative) repel each other. When two similarly charged combs are suspended from threads, they push each other apart. Just remember this simple rule: like charges repel, unlike charges attract.

7.2 Electric Force and Coulomb’s Law This force between charged objects is extremely important in the physical world, particularly at the atomic level. It is this interaction that holds atoms together and makes it possible for them to exist. In each atom, the positively charged protons in the nucleus exert attractive forces on the negatively charged electrons.

7.2 Electric Force and Coulomb’s Law The electric force on each electron provides the centripetal force that keeps it in its orbit, much as the gravitational force exerted by the Sun keeps Earth in its orbit. The forces between the atoms in many compounds arise because opposite charges attract.

7.2 Electric Force and Coulomb’s Law For example, when salt is formed from the elements sodium and chlorine, each sodium atom gives up an electron to a chlorine atom. The resulting ions exert attractive forces on one another because they are oppositely charged. Matter as we know and experience it would not exist without the electrical force.

7.2 Electric Force and Coulomb’s Law Recall Newton’s law of universal gravitation, which gives the size of the force acting between two masses. The corresponding law for the electrical force, Coulomb’s law, is very similar. Coulomb’s Law: The force acting on each of two charged objects is directly proportional to the net charges on the objects and inversely proportional to the square of the distance between them:

7.2 Electric Force and Coulomb’s Law The constant of proportionality in SI units is: 9 × 10 9 N-m 2 /C 2 Therefore, in SI units, with F in newtons, q 1 and q 2 in coulombs, and d in meters.

7.2 Electric Force and Coulomb’s Law The force on q 1 is equal and opposite to the force on q 2, by Newton’s third law of motion. Note that if both objects have the same kind of charge (both positive or both negative), then the force F is positive. This indicates a repulsive force. If one charge is negative and the other positive, then the force F is negative, indicating an attractive force.

7.2 Electric Force and Coulomb’s Law If the distance between two charged objects is doubled, then the forces are reduced to one-fourth their original values.

7.2 Electric Force and Coulomb’s Law Perhaps it is not a surprise that Coulomb’s law has the same form as Newton’s law of universal gravitation. After all, mass and charge are both fundamental properties of the particles that comprise matter. We must remember, however, that the (gravitational) force between two bodies because of their masses is always an attractive force, whereas the (electrostatic) force between two bodies from their electric charges can be attractive or repulsive, depending on whether or not they have opposite charges.

7.2 Electric Force and Coulomb’s Law Also, all matter has mass and so experiences and exerts gravitational forces, whereas the electrostatic force normally acts between objects only when there is a net charge on one or both of them. Generally, when two objects have electric charges, the electrostatic force between them is much stronger than the gravitational force. For example, the electrostatic force between an electron and a proton is about 10 39 times as large as the gravitational force between them.

7.2 Electric Force and Coulomb’s Law It is possible for a charged object to exert a force of attraction on a second object that has no net charge. This is what happens when a charged comb is used to pick up bits of paper or thread. Here the negatively charged comb attracts the nuclei of the atoms and repels the electrons.

7.2 Electric Force and Coulomb’s Law The orbits of the electrons are distorted so that the electrons are, on the average, farther away from the charged comb than the nuclei.

7.2 Electric Force and Coulomb’s Law This results in a net attractive force because the repulsive force on the slightly more distant, negatively charged electrons is smaller than the attractive force on the closer, positively charged protons. The process of inducing a small charge separation (or displacement) between the nucleus of an atom and its electrons is called polarization.

7.2 Electric Force and Coulomb’s Law Some molecules are naturally polarized—that is, they have a net negative charge displaced to one side of the net positive nuclear charge. They are called polar molecules. Water molecules have this property. If a polar molecule is free to rotate—as in a liquid—it will be attracted to a charged object. Its side with the charge opposite that on the object will turn toward the object, and the attractive force on that side will be stronger than the repulsive force on the other side.

7.2 Electric Force and Coulomb’s Law The electrostatic force is another example of “action at a distance.” As with gravitation, the concept of a field is useful. In the space around any charged object, there is an electric field. This field is the “agent” of the electrostatic force: it will cause any charged object to experience a force.

7.2 Electric Force and Coulomb’s Law The electric field around a charged particle is represented by lines that indicate the direction of the force that the field would exert on a positive charge. The electric field lines around a positively charged particle point radially outward, and the field lines around a negatively charged particle point radially inward.

7.2 Electric Force and Coulomb’s Law The strength of an electric field at a point in space is equal to the size of the force that it would cause on a given charged object placed at that point, divided by the size of the charge on the object.

7.2 Electric Force and Coulomb’s Law Where the field is strong, a charged object will experience a large force. The strength of the electric field is indicated by the spacing or density of the field lines: where the lines are close together, the field is strong. The electric field around a charged particle is clearly weaker at greater distances from it.

7.2 Electric Force and Coulomb’s Law Any time a positive charge is in an electric field, it experiences a force in the same direction as the field lines. A negative charge in an electric field feels a force in the opposite direction of the field lines.

7.2 Electric Force and Coulomb’s Law Perhaps you have had the experience of walking across a carpeted floor and receiving a shock when you touched a metal doorknob. This is more likely to happen in winter than in summer because the relative humidity is usually lower then, and electrostatic charging takes place more readily.

7.2 Electric Force and Coulomb’s Law The shock results from charges flowing between you and the doorknob, and it may be accompanied by a visible spark. Air normally does not allow charges to flow through it. A spark occurs when there is an electric field strong enough to ionize atoms in the air. Freed electrons accelerate in a direction opposite to the direction of the electric field, and positive ions accelerate in the same direction as the field. The electrons and ions pick up speed and collide with other atoms and molecules, ionizing them or causing them to emit light.

7.2 Electric Force and Coulomb’s Law Lightning is produced in this same way on a much larger scale as Benjamin Franklin demonstrated using kites, keys, and metal rods in the middle of the 18th century.

7.2 Electric Force and Coulomb’s Law Although most of the electrical devices we rely on make use of electric currents, some depend primarily on electrostatics. One important example of the latter is the electrostatic precipitator, an air-pollution control device.

7.2 Electric Force and Coulomb’s Law Tiny particles of soot, ash, and dust are major components of the airborne emissions from power plants that burn fossil fuels and from many industrial processing plants. Electrostatic precipitators can remove nearly all of these particles from the emissions. The flue gas containing the particles is passed between a series of positively charged metal plates and negatively charged wires.

7.2 Electric Force and Coulomb’s Law

The strong electric field around the wires creates negative ions in the particles. These negatively charged particles are attracted by the positively charged plates and collect on them. Periodically, the plates are shaken so the collected soot, ash, and dust slide down into a collection hopper. This “fly ash” must then be disposed of, but sometimes it has its own uses—for example, as a filler in concrete.

7.2 Electric Force and Coulomb’s Law Electronic signs that behave like electronically erasable paper make use of electric fields to form letters and other images. One type, called SmartPaper, consists of millions of tiny beads between two thin plastic sheets.

7.2 Electric Force and Coulomb’s Law One side of each bead is a particular color and negatively charged, and the other side is a contrasting color and positively charged. An electric field exerts opposite forces on the two sides, causing the beads to rotate until they are aligned with the field. Letters are formed on the electronic paper by selectively applying upward and downward electric fields at different places so that parts of the display are one color and the rest are the other color.

Concept Map 7.1

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