20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241

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1 Chapte 0 Electicity ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge whee these lines ae moe closely spaced. Video Encyclopedia 17 #8 Van De Gaaff with Steames 0-9 ELECTRIC POTENTIAL Goals Define electic potential enegy and electic potential. Show the similaity between electic potential enegy and gavitational potential enegy. Define a volt. (Poblem Solving) Calculate the electic potential diffeence between two points. (Poblem Solving) Develop the equation fo the electic field between two paallel plates held at a fixed potential diffeence. Content Electic potential enegy has the same chaacteistics as gavitational potential enegy. Like gavity, fo example, the zeo point is an abitaily defined point. An expeimente's concen is with the diffeence in the electic potential enegy values between two points. The electic potential (measued in volts) is defined as the electic potential enegy divided by the chage on the object. Teaching Tips This section is not needed fo the est of the book, except that the students should be familia with the concept of voltage if you plan to cove electic cuents in the next chapte. Physics on You Own Students expeiment with the spaks ceated when they touch doo knobs. They ae asked to estimate the electic potential fom the length of the spak. Poblem Solving 0.4 We calculate the electic potential diffeence between two points fom the wok done in moving a chaged paticle between the two points. We develop the equation fo the electic field between two paallel plates held at a fixed potential diffeence and wok an example in which an electon is stopped by this electic field. Compute Animations Active igue Animations ae available on the Multimedia Manage Instucto s Resouce CD. They ae oganized by textbook chapte, and each animation comes within a shell that povides infomation on how to use the animation, exploation activities, and a shot quiz. Answes to the Conceptual Questions 1. Because the chage does not flow along the object, the object must be an insulato.. The glass od is an insulato so the only chage tansfeed to the ball is at the point of contact on the od.

2 4 Chapte 0 Electicity 3. Any excess chage placed on the metal od will flow feely to all points on the suface of the od. 4. This will not wok unless you insulate the od fom you hand because the od is a conducto. 5. On a humid day the moistue in the ai allows some of the accumulated chage to leave the balloon. 6. The humidity in Honolulu allows chage to leak off chaged objects. 7. To pevent the build up of chage that might cause spaks. 8. The washing pocess leaves some of the clothes with a net electic chage. 9. The inteactions with the fu and plastic must have poduced opposite chages on the od. (It is also possible that one of the ods is not chaged.). The silk has a negative chage because its chage must be opposite the chage on the glass od. 11. We have positive, negative, and neutal because neutal is made up of equal amounts of positive and negative. Neutal objects do not attact each othe because of the cancellation of foces aising fom the positive and negative chages. 1. A thid kind of chage would be attacted to the two known kinds of chages and epelled by itself. 13. Showing you classmate that the noth pole of a magnet is attacted to both a chaged glass od and a chaged ubbe od but not a neutal wooden od demonstates that it is electically neutal. 14. If magnetic poles esulted fom diffeent electic chages, we would expect the two poles of the magnet to behave oppositely. That this does not happen is evidence that magnets ae electically neutal. Both poles ae attacted to the ubbe od. 15. They will epel each othe because all thee balls must have the same chage. 16. Balls and 3 may o may not be chaged. If ball 1 is chaged, but balls and 3 ae not, then balls and 3 will neithe attact no epel each othe. If ball is chaged, but ball 3 is not, they will attact each othe. If both ball and ball 3 ae chaged, then they must have the same type of chage (as they both attacted ball 1), so they would in this case epel each othe. 17. The two positive chages and the two negative chages yield a total chage of zeo. 18. A negatively chaged object could have eithe an excess of negative chage o a deficiency of positive chage. 19. The balloon sticks to the wall by inducing a chage in the wall. 0. The chage on the comb emains the same sign. The bits of pape stat out neutal and ae attacted by induction. When they come into contact with the comb, they acquie some chage fom the comb and ae epelled. 1. The induced chages on the nea sides ae always opposite those on the chaged object, poducing attactions.. a) By attacting positive chages to the nea side and/o epelling negative chages to the fa side of the object. b) By inducing a chage sepaation in the atoms and molecules in the object, o by otating pola molecules. 3. Bing the chaged od next to the electoscope. If the leaves get close togethe, the od is negative. If the leaves get fathe apat, the od is positive. 4. When you slowly bing the negatively chaged od nea an electoscope, the leaves will move fathe apat if they ae negatively chaged and close togethe if they ae positively chaged. 5. Touch the od to the electoscope. 6. Bing the negatively chaged od nea the electoscope but don't touch it. Touch the electoscope with you hand, emove you hand, and then the od. 7. The negative chages flow though the hand to gound, neutalizing the electoscope. 8. The positive chage on the electoscope attacts negative chage to the suface of you neutal hand. This induced chage educes the sepaation between the leaves. 9. Sphee B causes the deflection to decease in both cases so B must be neutal. Sphee A must be negatively chaged because only a negative chage could incease the deflection of the leaves of a

3 Chapte 0 Electicity 43 negatively chaged electoscope. 30. Using a negative od to chage the electoscope by induction leaves the electoscope positively chaged. Binging a positively chaged od nea will incease the sepaation of the leaves. 31. Touching a chaged sphee to a neutal one yields two sphees with 1/ chage on each one. Using two neutal sphees yields chages of 1/3. And so on. 3. When identical sphees ae touched, the esulting chage on each sphee is the aveage of the two oiginal chages. Touching A and C esults in each having chage +1q. Now, touching C and B esults in both being neutal. 33. Diagam d indicates foces that ae equal and opposite to each othe, as equied by Newton s thid law. 34. The electic foce expeienced by object B is equal to newtons by Newton s thid law. 35. The foce deceases by a facto of nine. 36. The foce inceases by a facto of fou. 37. The foce would tiple. 38. The foce inceases by a facto of fou. 39. The foce of C on A is to the ight and is fou times geate than the foce of B on A, which is down. Adding these vectos poduces a foce in the diection indicated by choice At point A the electic foces ae the same magnitude and oppositely diected. The net foce at A is zeo. At B, the electic foces ae the same magnitude. One points to the ight and up; the othe to the left and up at the same angle. Adding these vectos togethe poduces a foce in the up diection. 41. The gavitational foce is always attactive, electic chage is not popotional to inetial mass, the elementay electic chage comes in one size, and gavity is much weake. 4. The gavitational and electic foces have the same invese-squae popotionality between stength and distance. 43. The two of you have vey little net electic chage and the gavitational foce is too weak. 44. The Sun, moons, and planets have almost no net electic chage. 45. Even if the objects all have the same chage, they have diffeent masses and, theefoe, diffeent acceleations. 46. In the atio of the two foces the distances cancel. This occus because the two foces have the same dependence on distance. 47. The electic foce is popotional to the chage of the object in the electic field. If the chage doubled, the foce would double to 30 newtons diected to the left newtons diected to the ight. 49. The sepaation of the electic field lines indicates the stength of the electic field. Since the sepaation is unifom, the chage would expeience the same foce at any point between the plates. 50. The same foce would act on the paticle fo twice the distance giving it twice the kinetic enegy. It would stike the negative plate at a speed geate than v. 51. The foces have the same size but opposite diections with the foce on the poton being upwad. 5. The acceleations have diffeent sizes because the masses ae diffeent; the atio of the acceleations is equal to the invese atio of thei masses. They have diffeent diections because the chages have opposite signs. 53. The foce vectos would be tangent to the field lines and the magnitudes of the foces would ank b>a>c=d, as seen by the local density of field lines. 54. The foce vectos would point tangent to the field lines, but in the opposite diection. The moving chage must be negative, as it expeiences acceleation (and hence net foce) opposite the diection of the field lines. 55. The electic field lines ae close togethe in the egion between A and B than in the egion between C and D. The electic field is theefoe geate in the egion between A and B.

4 44 Chapte 0 Electicity 56. Because the electic field is stonge in the egion between A and B, one would have to do moe wok to move a chage between these two points meaning the potential diffeence is geate. 57. The speed at point B is geate than v o. The change in electic potential is negative and, because the chage is positive, the change in electic potential enegy is also negative. To conseve enegy, the change in kinetic enegy must be positive. 58. The speed at point B is less than v o. The change in electic potential is negative but, because the chage is negative, the change in electic potential enegy is positive. To conseve enegy, the change in kinetic enegy must be negative. 59. The electic potential at a point in space is equal to the wok equied to bing 1 coulomb of positive chage fom the location chosen as zeo to the point. 60. The electic potential enegy of an object at a point in space is equal to the wok equied to bing that object fom the location chosen as zeo to the point. 61. Just like a ball moving in a gavitational field, the poton will move to lowe its electic potential enegy. It also moves towad a lowe electic potential. 6. Just like a ball moving in a gavitational field, the electon will move to lowe its electic potential enegy. Howeve, due to its negative chage, it moves towad a highe electic potential. Answes to the Execises 1. Qnet = 11e e = e = 1.6 C. Qnet = 53 e 54 e = e = 1.6 C 3. (94 potons)(1.6 C/poton) = C 4. (-1 C)/(-1.6 C/electon) = electons 1 ( 3C) ( 6C) 5. = k = N C ( m) e kq Q N m ( 4C)( 4C) 1 9 = = 9 = m g e g C ( 3.6 N) N 31.6 ( C) 11 C ( 1.8 m) N ( 1.6 C) C ( 1 m) 9 ( 9 N m /C )( 1.6 C) 11 7 ( 6.67 N m / kg )( kg) 9 ( 9 N m /C )( 1.6 C) ( 6.67 N m / kg )( 9.11 kg) = k = 9.13 N attactive = k = 9.3 N attactive kq Q 1 = = Gmm 1 kq Q Gmm = =

5 Chapte 0 Electicity 45 4 N noth 11. E = = = 800 N C ( noth) Q 5mC = QE = 0 mc 800 N C ( noth) = 16 N ( south) 5 N ( west) 1. E = = = 150 N C ( east) Q 0 mc The electic field is the same at this location independent of what chage is placed thee. It will still be 150 N/C (east). 3 Q C 13. E = k = N C towad the chage C 4 m Q 4C 9 E = k = 9 9 N C away fom the chage C ( m) 19 ( ) Q C 11 E = k = 9.16 N outwad C m Q 1.6 C 11 E = k = N C C 5.3 m 11 away fom the poton Q1 Q m 4C E = k = N C towad the -C chage C ( 1m) Q N ( 1.6 C) E k C ( m) 19. = QE = ( ) ( ) = N C C 5 N C 8 N 16 8 N 11 a = = = 4.79 m s 7 m 1.67 kg 0. QE = C 5 N C 8 N 16 8 N 14 a = = = 8.78 m s 31 m 9.11 kg 1. PEB = PEA + PE = PEA KE = 40 J 50 J = J. PE = PE PE = J 40 J = 50 J AB B A PEAB 50 J VAB = = = 5 V Q C 3. W Q V = = 3 3 C 1 V 4 J 4 mj 4. W = Q V = ( ) = 5. V Ed 6. d 3mC 9V 9V 0 = = 30,000 V cm 1.3 cm = 39,000 V 5 6 V 4 3 V cm V = = = E 0 cm towad the electon

6 46 Chapte 0 Electicity Answes to the Poblems in Poblem Solving C 4 = electons = 1.6 C electon C = = 6.6 action emoved = = C Q net N emoved ( 9)( 1.6 C) 9 ( 1.6 C) 9 ( 1.6 C) 1 6 = k = 8.99 =.1 N C 0.1 m 1 9 = k = N C 0. m 1 8 = k = N C ( 1m) ( 1.6 C) = k = 8.99 = 9.1 N C 5 m The foce is the same size, but in the opposite diection. ( C) ( m) 1 9 = k = 8.99 = 8.99 N C 1 9 = v + h + d = + ( 8.99 N) = 1.7 N ( 3C) ( 1m) 1 = k = 8.99 = 8.09 N C 3 N ( C) ( 1.6 C) = + = 8.09 N N = 1.14 N 11 v h Q Q a = = k = 8.99 = 3.51 m s m m C 9.11 kg 0.03 m ( ) ( 1.6 C) Q Q N a = = k = m m C 9.11 kg 5 m Q e g k Q = = G M M 1 GM M = = k 1 7 = 3.7 C m s 1 ( N m kg ) ( kg) ( 7.36 kg) 8.99 N m C Theefoe, Q = C 8

7 Chapte 0 Electicity Q e g k Q = = G M M 1 1 ( N m kg )( 70 kg) GM M = = = 3.64 C k 8.99 N m C Theefoe, Q = C N ( noth) 3 E = = = 9.38 N C south Q 1.6 C E 4 1. N noth 1 5 = = = N C south Q1 6 C ( N m C ) ( 3 6 C) = QE = 1.6 C N c south = 3. N south kq = = = m 4 E 5.0 N C 9 9 ( 8.99 N m C ) ( 7 C) kq E = B = = 5 N C away fom ball B ( 0.5 m) 17. Both foces act in the same diection, so we add the magnitudes of the two foces. Q1 Q 4k E = E1+ E = k + k = ( Q1+ Q) 1 1 d d d 9 ( ) N m C 1 8 C N/C ( 0.16 m) 18. The foces act in opposite diections, so we subtact the magnitudes of the two foces. Q1 Q 4k E = E1 E = k k = ( Q1 Q) 1 1 d d d 19. a 0. E 9 ( ) N m C e ( 0.1 m) e C 1.44 N/C 9 ( 8.99 N m C ) ( 1.6 C) 31 1 ( 9.11 kg)( m) k Q = = = = m m ( 0.1 kg)( 9.8 m s ) mg = = = 3 Q C 1. V = V + W = 50 J + 30 J = 80 J B. Q A W 75 J = = = 0.5 C V 300 V 3. W = Q V = = 4. W Q V 5. W Q V 490 N C 4 C 1 V 48 J ; it is the same..53 m s 8 = = C 4 V 4 V = 0 ; the intemediate location does not matte. = = 3C 0V 5 V = 45J; 45 J

8 48 Chapte 0 Electicity 6. W Q V 7. d = C 1 V 1.9 J 6 V 4 3 V cm V = = = E 33.3 cm 8. V Ed = = 30,000 V cm 5 cm = 150,000 V V 1 N m = = N m m C C N m CV = C = N m = J C V = Ed = 7500 N/C 0.05 m = 375 V V 1 V d = = = E 1400 N/C m 8.87 mm