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Unformatted text preview: CHAPTER 21: Electric Charges and Electric Field Responses to Questions
1. Rub a glass rod with silk and use it to charge an electroscope. The electroscope will end up with a net positive charge. Bring the pocket comb close to the electroscope. If the electroscope leaves move farther apart, then the charge on the comb is positive, the same as the charge on the electroscope. If the leaves move together, then the charge on the comb is negative, opposite the charge on the electroscope. The shirt or blouse becomes charged as a result of being tossed about in the dryer and rubbing against the dryer sides and other clothes. When you put on the charged object (shirt), it causes charge separation within the molecules of your skin (see Figure 21-9), which results in attraction between the shirt and your skin. Fog or rain droplets tend to form around ions because water is a polar molecule, with a positive region and a negative region. The charge centers on the water molecule will be attracted to the ions (positive to negative). See also Figure 21-9 in the text. The negatively charged electrons in the paper are attracted to the positively charged rod and move towards it within their molecules. The attraction occurs because the negative charges in the paper are closer to the positive rod than are the positive charges in the paper, and therefore the attraction between the unlike charges is greater than the repulsion between the like charges. 2. 3. 4. -+
+++++++ -+ -+ -+ 5. A plastic ruler that has been rubbed with a cloth is charged. When brought near small pieces of paper, it will cause separation of charge in the bits of paper, which will cause the paper to be attracted to the ruler. On a humid day, polar water molecules will be attracted to the ruler and to the separated charge on the bits of paper, neutralizing the charges and thus eliminating the attraction. The net charge on a conductor is the difference between the total positive charge and the total negative charge in the conductor. The “free charges” in a conductor are the electrons that can move about freely within the material because they are only loosely bound to their atoms. The “free electrons” are also referred to as “conduction electrons.” A conductor may have a zero net charge but still have substantial free charges. Most of the electrons are strongly bound to nuclei in the metal ions. Only a few electrons per atom (usually one or two) are free to move about throughout the metal. These are called the “conduction electrons.” The rest are bound more tightly to the nucleus and are not free to move. Furthermore, in the cases shown in Figures 21-7 and 21-8, not all of the conduction electrons will move. In Figure 21-7, electrons will move until the attractive force on the remaining conduction electrons due to the incoming charged rod is balanced by the repulsive force from electrons that have already gathered at the left end of the neutral rod. In Figure 21-8, conduction electrons will be repelled by the incoming rod and will leave the stationary rod through the ground connection until the repulsive force on the remaining conduction 6. 7. electrons due to the incoming charged rod is balanced by the attractive force from the net positive charge on the stationary rod. 8. The electroscope leaves are connected together at the top. The horizontal component of this tension force balances the electric force of repulsion. (Note: The vertical component of the tension force balances the weight of the leaves.) Coulomb’s law and Newton’s law are very similar in form. The electrostatic force can be either attractive or repulsive; the gravitational force can only be attractive. The electrostatic force constant is also much larger than the gravitational force constant. Both the electric charge and the gravitational mass are properties of the material. Charge can be positive or negative, but the gravitational mass only has one form. 9. 10. The gravitational force between everyday objects on the surface of the Earth is extremely small. (Recall the value of G: 6.67 x 10-11 Nm2/kg2.) Consider two objects sitting on the floor near each other. They are attracted to each other, but the force of static fiction for each is much greater than the gravitational force each experiences from the other. Even in an absolutely frictionless environment, the acceleration resulting from the gravitational force would be so small that it would not be noticeable in a short time frame. We are aware of the gravitational force between objects if at least one of them is very massive, as in the case of the Earth and satellites or the Earth and you. The electric force between two objects is typically zero or close to zero because ordinary objects are typically neutral or close to neutral. We are aware of electric forces between objects when the objects are charged. An example is the electrostatic force (static cling) between pieces of clothing when you pull the clothes out of the dryer. 11. Yes, the electric force is a conservative force. Energy is conserved when a particle moves under the influence of the electric force, and the work done by the electric force in moving an object between two points in space is independent of the path taken. 12. Coulomb observed experimentally that the force between two charged objects is directly proportional to the charge on each one. For example, if the charge on either object is tripled, then the force is tripled. This is not in agreement with a force that is proportional to the sum of the charges instead of to the product of the charges. Also, a charged object is not attracted to or repelled from a neutral object, which would be the case if the numerator in Coulomb’s law were proportional to the sum of the charges. 13. When a charged ruler attracts small pieces of paper, the charge on the ruler causes a separation of charge in the paper. For example, if the ruler is negatively charged, it will force the electrons in the paper to the edge of the paper farthest from the ruler, leaving the near edge positively charged. If the paper touches the ruler, electrons will be transferred from the ruler to the paper, neutralizing the positive charge. This action leaves the paper with a net negative charge, which will cause it to be repelled by the negatively charged ruler. 14. The test charges used to measure electric fields are small in order to minimize their contribution to the field. Large test charges would substantially change the field being investigated. 15. When determining an electric field, it is best, but not required, to use a positive test charge. A negative test charge would be fine for determining the magnitude of the field. But the direction of the electrostatic force on a negative test charge will be opposite to the direction of the electric field. The electrostatic force on a positive test charge will be in the same direction as the electric field. In order to avoid confusion, it is better to use a positive test charge. 16. See Figure 21-34b. A diagram of the electric field lines around two negative charges would be just like this diagram except that the arrows on the field lines would point towards the charges instead of away from them. The distance between the charges is l. 17. The electric field will be strongest to the right of the positive charge (between the two charges) and weakest to the left of the positive charge. To the right of the positive charge, the contributions to the field from the two charges point in the same direction, and therefore add. To the left of the positive charge, the contributions to the field from the two charges point in opposite directions, and therefore subtract. Note that this is confirmed by the density of field lines in Figure 21-34a. 18. At point C, the positive test charge would experience zero net force. At points A and B, the direction of the force on the positive test charge would be the same as the direction of the field. This direction is indicated by the arrows on the field lines. The strongest field is at point A, followed (in order of decreasing field strength) by B and then C. 19. Electric field lines can never cross because they give the direction of the electrostatic force on a positive test charge. If they were to cross, then the force on a test charge at a given location would be in more than one direction. This is not possible. 20. The field lines must be directed radially toward or away from the point charge (see rule 1). The spacing of the lines indicates the strength of the field (see rule 2). Since the magnitude of the field due to the point charge depends only on the distance from the point charge, the lines must be distributed symmetrically. 21. The two charges are located along a line as shown in the 2Q diagram. Q (a) If the signs of the charges are opposite then the point on the line where E = 0 will lie to the left of Q. In that region ℓ the electric fields from the two charges will point in opposite directions, and the point will be closer to the smaller charge. (b) If the two charges have the same sign, then the point on the line where E = 0 will lie between the two charges, closer to the smaller charge. In this region, the electric fields from the two charges will point in opposite directions. 22. The electric field at point P would point in the negative x-direction. The magnitude of the field would be the same as that calculated for a positive distribution of charge on the ring: E= 1 4πε o x + a 2
2 ( Qx ) 1/ 2 23. The velocity of the test charge will depend on its initial velocity. The field line gives the direction of the change in velocity, not the direction of the velocity. The acceleration of the test charge will be along the electric field line. 24. The value measured will be slightly less than the electric field value at that point before the test charge was introduced. The test charge will repel charges on the surface of the conductor and these charges will move along the surface to increase their distances from the test charge. Since they will then be at greater distances from the point being tested, they will contribute a smaller amount to the field. 25. The motion of the electron in Example 21-16 is projectile motion. In the case of the gravitational force, the acceleration of the projectile is in the same direction as the field and has a value of g; in the case of an electron in an electric field, the direction of the acceleration of the electron and the field direction are opposite, and the value of the acceleration varies. 26. Initially, the dipole will spin clockwise. It will “overshoot” the equilibrium position (parallel to the field lines), come momentarily to rest and then spin counterclockwise. The dipole will continue to oscillate back and forth if no damping forces are present. If there are damping forces, the amplitude will decrease with each oscillation until the dipole comes to rest aligned with the field. 27. If an electric dipole is placed in a nonuniform electric field, the charges of the dipole will experience forces of different magnitudes whose directions also may not be exactly opposite. The addition of these forces will leave a net force on the dipole. ...
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This note was uploaded on 03/22/2009 for the course PHY 54L taught by Professor Thomas during the Spring '09 term at Duke.
- Spring '09