Chapter 16 Answers

All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.

6.   9.2 N

12.   83.8 N away from the center of the triangle

16.   5.71 x 10¹³ C

18.   0.21 nm

26.   3.15 x 10⁸ N/C toward the negative charge

28.   6.22 x 10^-10 C

36.   The gravitational field is 0 at a point 90% of the way from the earth to the moon. Note that only the solution of the quadratic equation which is between the earth and moon is physically valid. The other solution is on the other side of the moon, where the forces have the same magnitude, but the directions are the same, so they don't cancel.

38. (a)   8.83 x 10⁶ m/s,   (b)   a = 3.3x10¹⁴ g

2. A shirt or blouse taken from the clothes drier has been rubbing against other clothes, which could cause a transfer of electrons from one material to another, leading to a charge on the shirt which could cause it to cling to you.

3. Fog or rain droplets tend to form around ions or electrons in the air because water is a polar molecule. The outer electrons tend to congregate around the oxygen atom more than around the hydrogen atoms, leading to a positive charge on the hydrogen atoms and negative charge on the oxygen atom. See Figure 16-4 in the text. A free electron in the air will attract the hydrogen atoms in the water vapor. A positive ion would attract the oxygen.

4. Although the paper is neutral, the electrons can be pulled a little bit away from the positive nuclei, toward the positively charged rod. Then the electrons in the paper are closer to the rod than the nuclei on the average, so they are attracted more strongly by the charge in the rod than the positive nuclei are repelled (remember the inverse square law). This gives a net attractive force on the paper, even though the paper is electrically neutral.

5. A plastic ruler that has been rubbed will lose some of its electrons, and try to pull on the electrons in the paper. See question 4 for the detailed explanation. This is difficult on a humid day because water vapor will be attracted to the ruler and tend to carry away the excess charge, since water is a polar molecule. See question 3.

6. The net charge on a conductor is the algebraic sum of all the charges on the conductor, which normally would be the sum of all the positive charges from the protons in the nuclei, minus the sum of all the negative charges of the electrons in the atoms, plus any extra charges which may have been deposited on the conductor. The free charges are the ones that are in orbitals which are loosely bound to the individual atoms and are shared by the atoms throughout the conductor. Only these can move about freely to conduct electricity.

7. Only some of the electrons in a metal move when a charged rod is placed nearby, because most of the electrons are in orbitals which are tightly bound to the individual atomic nuclei, so they cannot leave those atoms. See also question 6.

8. Gravity balances the electrostatic repulsion of the leaves in the electroscope. The leaves rise until their electrostatic repulsion is balanced by their weight.

9.Newton's law is always attractive, while Coulomb's law can be either attractive or repulsive. The source of gravitational attraction is mass, which is always positive. The source of electric attraction or repulsion is charge, which can have either a positive or negative charge. Also, the gravitational force is very weak, requiring a large amount of the source (mass) to be noticeable, while even very small charges can make a strong electric field.

10. We are not normally aware of the gravitational attraction between ordinary objects (not planet-sized) because it is very weak. We are not aware of the electrical force because positive and negative charges tend to pair together to make neutral objects, so the net electrical force is nearly canceled, making it very weak on the average for normal neutral matter.

11. The electrical force is conservative, because it depends only on the relative positions of the charges, and the work done to move a charge through the electric field is independent of the path taken, only on the initial and final condition. This is what allows an electric potential to be defined.

12. The fact that equal and opposite charged attract rules out the possibility that the force could be proportional to (Q₁ + Q₂), since in that case, there would be no force between the charges.

13. When the paper touches the ruler, some charge is transferred from the ruler to the paper. The ruler and paper then have the same sign charge, so they repel.

14. We use small test charges when measuring electric fields so the test charge does not change the distribution of the other charges which are producing the field. This is especially important when we are measuring the field near conductors, since a big test charge could induce a different charge distribution on the conductor than it would have in the absence of the test charge.

15. We could just as well use a negative test charge to determine an electric field, but then the Electric field vector would point opposite the direction of the force on the test charge.

16. The field lines would look like those in Figure 16-29 (b) in the text, but the arrows would point toward the charges rather than away, since they are negative.

17. The electric field is strongest to the right of the positive charge, because that is where the field lines are closest together. The field is weakest to the left of the positive charge, since the field lines are furthest apart there.

18. The arrows at A and B would be drawn in the same direction as the nearby arrows on the field lines. At point C, there is no net electric force, since the charge is repelled equally by the charges to the left and the right. So no arrow goes at point C: the electric field is 0 there. The field is strongest where the lines are closest together, so in order of decreasing field strength, the points would be A, B, C.

19. Electric field lines show the direction of the force acting on a test charge placed at that point. If the lines crossed, the direction of force would be undefined. Physically, there is no way for that to happen. The electric field has to push the charge somewhere. Electric field lines meet only at charges.

20. The field lines show the direction of force acting on a test particle. Since force is proportional to acceleration (Newton's second law), the acceleration of the test charge is along the field line. The velocity need not be in the same direction as the acceleration. (Remember uniform circular motion, for example, where the velocity and acceleration are actually perpendicular.)

21. When the positive test charge is brought close to the positively charged conducting sphere, it will repel charges on the sphere, reducing the electric field near the test charge q₀. So the value F₀/q₀ measured will be less than the value of E in the absense of the test charge. This is an example of why it is important to minimize the size of the test charge when attempting to measure an electric field. A big test charge disturbs the field it is attempting to measure.