chap174 - O Alarge negative charge(c The electric eld...

This preview shows page 1 - 11 out of 11 pages.

Image of page 1

Subscribe to view the full document.

Image of page 2
Image of page 3

Subscribe to view the full document.

Image of page 4
Image of page 5

Subscribe to view the full document.

Image of page 6
Image of page 7

Subscribe to view the full document.

Image of page 8
Image of page 9

Subscribe to view the full document.

Image of page 10
Image of page 11

Unformatted text preview: . O Alarge negative charge (c) The electric field remains constant and the charge on the plates decreases. ((1) Both the electric field and the charge on the plates decrease. . Q A capacitor has been charged with +Q on one plate and —Q on the other plate. Which of these state- ments is true? (a) The potential difference between the plates is QC. (b) The energy stored is %Q AV. (c) The energy stored is %Q:C. (d) The potential difference across the plates is QIHZC). to) None of the previous statements is true. . Two solid metal spheres of different radii are far apart. The spheres are connected by a fine metal wire. Some charge is placed on one of the spheres. After electro- static equilibrium is reached, the wire is removed. Which of these quantities ti ill be the some for the two spheres? (a) the charge on each sphere (b) the electric field inside each sphere, at the same dis- tance from the center of the spheres (c) the electric field just outside the surface of each sphere (d) the electric potential at the surface of each sphere (e) both (b) and (c) if) both (b) and (d) (g) both (a) and (c) -—Q is located in the vicinity of points A and B. Suppose a positive charge +q is moved at constant speed from A to B by an external agent. Along which of the paths shown in the figure will the Work done by the field be the greatest? (at path 1 (b1 path 2 (c) path 3 (d) path 4 (e) Work is the same along all four paths. . A tiny charged pellet of mass m is suspended at rest between two horizontal, charged metallic plates. The lower plate has a positive charge and the upper plate has a negative charge. Which statement in the answers here is not true? EW ‘1'“??? "El-'91”:- ééébeaééoeaéfifieaa t "-m (a) The electric field between the plates points vertically upward. (b) The pellet is negatively charged. (c)The magnitude of the electric force on the pellet is equal to mg. (d) The plates are at different potentials. I - a Two positive 2.0 pc point charges are placed as shown in part (a) of the figure. The distance from each charge to the point P is 0.040 m. Then the _———_ PROBLEMS 647 charges are rearranged as shown in part (b) of the fig- ure. Which statement is now true concerning E and V at point P? :nac T 0 040 In 0.040 m 0.040 m 0.040 at P 2.0 tic 2.0}1C P 3.0 [1C (at th) (21) The electric field and the electric potential are both zero. (b) E = 0 but V is the same as before the charges v. ere moved. (c) it" = 0. but E is the same as before the charges Were moved. ((1) E is the same as before the charges were moved. but V is less than before. (e) Both 73 and V have changed and neither is zero. 11. fl lnthediagram.wltich l7: _. two points are closest 3' to being at the same D . . i potenttal P I (am and D (b) B and C (c) B and D (dM and C‘ l2. 6 lntltediagram.which MUitiPIE'ChDiCEQUEStiOI‘IS point is at the lowest 11 and 12 potential? (10.4 (b) B (c) C (d) 1) Problems 6 Combination conceptualfltuantitative probletn e Biomedical application Challenging Blue it Detailed solution in the Student Solutions Manual Cl. 2 Problems paired by concept mud Text website interactive or tutorial 17.1 Electric Potential Energy I. in each of five situations. two point charges (Q.. (2;) are separated by a distance :1. Rank them in order of the electric potential energy. from highest to lowest. ('4) Qt = 1 11C.Qg=211C.d= l m (b)Q1=2PC-Q1= -l|1C.rl=lm (C)Q|=2|1C,Qg= —4ttC,d=2m ((lth=—:2 C. =-2t1C.d=2m l1 2 (B)Qt=4tLC.Q3=—2ttC,d=4m 648 CHAPTER 17 Electric Potential ‘. 1g . Two point charges. +5.0 pC Q=+5.0 jJ.C q=—2.0 ac IS. In the diagram, how much work is done by the electric and —2.0 11C, are separated 3|; 3 field as a third charge q] = +2.00 nC is moved froth" by 5.0 m. What is the electric 7— ": 5'0 m I point b to point c'? " potential energy? 3. O A hydrogen atom has a single proton at its center and a single electron at a distance of approximately 0.0529 nm from the proton. (a) What is the electric potential energy in joules? (b) What is the significance of the sign of the answer? 17.2 Electric Potential Unless stated otherwise. we assign the potential due to a: point charge to be zero at an infinite distance from the charge-”f 4. How much work is done by an applied force that moves 16' A point charge :1 = +10 nC moves through a potential. two charges of 6.5 ttC that are initially very far apart to a distance of4.5 cm apart? . The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of l.() I'm? . Three point charges are 5.51m located at the corners of T a right triangle as shown '3‘?“ difference AV = v — vi = +25 v. What is the changg- in the electric potential energy? . An electron is moved from point A. where the electric? potential is Va = —240 V, to point B. where the electric potential is VB = —360 V. What is the change in the'. electric potential energy? ' . Find the electric field and the potential at the center of a' square of side 2.0 cm with charges of +9.0 ttC at each corner. +9.0 uC +9.0 uC in the figure. How much — a h work does it take for an 4.5.1:: mm 2.5 “C 1 external force to more 2.0cm the charges apart until they are very far aw ay from one 1 another? _. ‘1 " Problems 7-10. Two point charges ( + l().0 11C and —- 10.0 nC) +9“ "C +9 (T “C are located 8.00 cm apart. For each problem. let U = 0 when j-— 3-0 CHI—e: nil ol‘ the charges are separated by infinite distances. _ _ 7. What is the potential energy for these two charges? l9. Find the electric field and the potential at the center of a_ 8. What is the potential energy if a a square ol'sidc 2.0 cm with a charge of +9.0 pC at one third point charge :1 = —4_2 nC is comer of the square and with charges of -3.0 uC‘ at the placed at point tr? 5.00 cm H.0(Icm remaining three comet's. 9. that is the potential energy if .a I, j, +9-0th '3-"PC third pornt charge q = —-'l.2 nC Is L4.t)0-'--tt)o-4.oo-' n I: placed at point h.’ ' cm ' cm cm i ‘1 10. What is the potential energy if :1 Problems 7-10 lotm third point charge q = —4.2 nC is placed at point t"? _L I 11. Find the electric potential energy for the litllowing “—3.0 at: —3.0pC array of charges: charge q. = +4.0 pC is located at 7—2pm” (.t'. _\') = (0.0. 0.0) in: charge q: = +3.0 0C is located at (4.0. 3.0) m: and charge q; :2 -1.0 ttC is located at 20. A charge of +2.0 mC is located at .t' = 0. y = 0 and a (0.0. 3.0) in. charge of --l.0 tnC is located at .\' = 0. y - 3.0 at. What 12. In the diagram. how much work is r_- is the electric potential due to these charges at a point done by the electric field as a third Wilh coordinates -" = 4-0 m. ." = 0‘3 charge ([3, = +2.00 nC is moved ll-Ocm ll-Ucm 2]. The electric potential at a distance of 20.0 cm from a from infinity to point a? a In I: a; point charge is +1.0 kV (assuming l” = 0 at infinilyl-. I}. In the diagram, how much work is - . I {a} is the point charge positive or negath e? (b) At what done by the electric-field as a third I 1 iijjjhfi-J distance is the potential +2.0 kV? (named tutorial: field . 4.00 cm 4.00 cm . . charge q, = +2.00 nC is moved and potential of point charge] from infinity ‘0 POim ”‘3 q. = +3.00 nC‘ 22. A spherical conductor with a radius of 75.0 cm has ant H. In the diagram. how much work is II: = *3-00'1‘3 electric field of magnitude 8.40 x [05 Wm just outside' done by the efectrt'cfield as a third Problems 12-15 its surface. What is the electric potential just outside the charge (13 = +2.00 nC is moved from point a to point 1:? surface. assuming the potential is zero far away from the conductor? 23.1% hollow metal sphere carries a charge of 6.0 uC. A second hollow metal sphere with a radius that is double the size of the first carries a charge of 18.0 ttC. The two spheres are brought into contact with each other, then separated. How much charge is on each? [Hinn In electrostatic equilibrium, the spheres must be at the same electric potential when in contact.] . An array of four chart-es :- _\ is arranged along the .r-axis at intervals of 1.0 m. (a) If two of the i~l.0tn~i'l.0m-:~l.0tn—. "- charges are +l.0 pC I and Mo are -l.0 uC. draw a configuration of these charges that minimizes the potential at .t' = 0. (b) if three of the charges are the same. q = +1.0 pC. and the charge at the far right is - l .0 ac. what is the potential at the origin? At a point P. a distance R1, Q“ from a positive charge Q", (4} the electric field has a mag- nitude E". = 100 MC and the electric potential is V” = 10 V. The charge is now increased by a fac‘ tor of three. becoming 390. {a} At what distance. Rh. from the charge 3Q“ will the electric field have the same Value. E = E“: and (h) at what distance. R\'. from the charge 3Q“ will the electric potential have the satne \alue, l’ = V“? 26. Charges of +2.0 nC and —l .0 ttC are located at opposite corners. A and C. respectively. of a square which is ID in on a side. What Him is the electric potential at a third ' corner. B. of the square ( it here there is no charge)? 5.“ reg. r A 1.0 m B 27. (a) Find the electric potential at points a and h for charges of +4.2 nC and —6.-l» nC located as shown . 1 . . W . tn the figure (b) hat is 1mm 12.0 the potential difference 1st; cm A‘V for a trip from I; to a; .6 ”0”" a? (c) How much work I- ' .- must be done by an exter- i mm" - nal agent to move a point charge of +l.50 nC from h to u? 28. (a) Find the potential at points a and b in the diagram for charges Q] = +2.50 nC and Q; = —2.50 nC. (b) How much work must be done by an external agent to bring a point charge (1 from infinity to point I)? a SQ I b (a: I I ~51) cnt ---5.0 cm -+-5.ll cm --' 29 (a) In the diagram, what are the potentials at points a and I)? Let V = 0 at infinity. (b) What is the change PROBLEMS in electric potential energy if a third charge (13 = +2.00 nC is moved from point a to point I)? 13-00”! '19 “m (If you have done Problem 14. u (it b It: compare your answers.) g8 00—1—4 30. (ailn the diagram. what are the 41.00::m em 4'00 cm potentials at points b and c? Let V = O at infinity. (b) What I“ =+l'l.()() HC is the change in electric poten- (”barium tial energy if a third charge Problems 29 and 30 q; = +2.00 nC is moved from point I: to point c? (If you have done Problem 15. com- pare your answers.) 3|. A 35.0 nC charge is placed at the origin and a 55.0 nC charge is placed on the +.t-axis, 2.20 cm from the origin. (a) What is the electric potential at a point hallway hetw een these two objects? (b) What is the electric potential at a point on the +.t'-axis 3.40 cm fnom the origin? {c} How much work does it take for an external agent to move a 45.0 nC charge from the point in (b) to the point in (a)? 17.3 The Relationship Between Electric Field and Potential 32. By rewriting each unit in terms of kilograms, tneters. seconds. and coulonihs. show that 1 NC = 1 Wm. 33. Rank points A-E in order of the potential, from highest to lowest. IIIIIIIIESIIII IIIHVIIINI'I n-urlg=snlnl IE‘! JIIIIEMII Ilhhfl!llnnll manna-=21Inl I'lIl‘IIIfl'III‘I IIIIIIIiII III Problems 34—36. A uniform electric field has magnitude 240 MC and is directed to the right. A particle with charge +4.2 nC moves in this field. For the given motion of the particle. find (a) the electric force that acts on the parti- cle: (b) the potential difference through which the particle moves; to) the change in the particle's potential energy: and td) the work done on the particle by the electric field. 34. The particle moves along a straight line from a to b. tfi| = 24:] we 35. The particle moves along a straight line from b to a. 36. The particle moves along the path shown from b to “I Problems 34-36 31'. An electron is suspended in a vacuum between two oppositely charged horizontal parallel plates. The sep- aration between the plates is 3.00 mm. (a) What are 650 38. “'39. {‘40. 4|. 43. CHAPTER 1? Electric Potential the signs of the charge on the upper and on the lower plates? (13) What is the voltage across the plates? In a region where there is an electric field. the electric forces do +8.0 x 10"‘9 J of work on an electron as it moves from point X to point Y. (a) Which point, X or 1’. is at a higher potential? (b) What is the potential differ- ence, VF — Vx, betWeen point 1’ and point X? Suppose a uniform electric field of magnitude 100.0 NIC exists in a region of space. How far apart are a pair of equipotential surfaces whose potentials differ by 1.0 V? Draw some electric field lines and a few equipotential surfaces outside a negatively charged hollow conducb ing sphere. What shape are the equipotential surfaces? Draw some electric field lines and a few equipotential surfaces outside a positively charged conducting cylin- der. What shape are the equipotential surfaces? . 9 It is believed that a large electric fish known as Torpedo occidenmh's uses electricity to shock its vic- tims. A typical fish can deliver a potential difference of 0.20 kV for a duration of LS ms. This pulse delivers charge at a rate of 18 Cls. (a) What is the rate at which work is done by the electric organs during a pulse? (b) What is the total amount of work done during one pulse? A positive point charge is located at the center of a hollow spherical metal shell with zero net charge. (a) Draw some electric field lines and sketch some equipotential surfaces for this arrangement. (b) Sketch graphs of the electric field magnitude and the potential as functions of r. Problems 44 and 45. A positively charged oil drop is injected into a region of uniform electric field between two oppositely charged, horizontally oriented plates spaced 16cm apart. f“ If the electric force on the drop is found to be 9.6 x 10‘16 N and the potential difference between the plates is 480 V, what is the magnitude of the charge on the drop in terms of the elementary charge 9? Ignore the small buoyant force on the drop. (correct tutorial: Millikan’s experiment) . If the mass of the drop is 1.0 x 10''5 kg and it remains stationary when the potential difference between the plates is 9.76 kV. what is the magnitude of the charge on the drop? (ignore the small buoyant force on the drop.) 17.4 Conservation of Energy for Moving Charges 46. Point P is at a potential of 500.0 kV. and point 5 is at a potential of 200.0 kV. The space between these points is evacuated. When a charge of +22 moves from P to S, by how much does its kinetic energy change? 47. 48. 49. 50. An electron is accelerated from rest through a poteng '-:' ' tial difference AV. If the electron reaches a Speed" I- of 7.26 x 106 mls. what is the potential difference? Be sure to include the correct sign. (Does the elec- '.- tron move through an increase or a decrease in . potential?) As an electron moves through a region of space, its . speed decreases from 8.50 x 105 mls to 2.50 x 10" mls. _ The electric force is the only force acting on the elec: tron. (:1) Did the electron move to a higher potential of a lower potential? (b) Across what potential difference did the electron travel? In each of six situations, a particle (mass or. charge q) moves from a point where the potential is Vi to a point where the potential is Vr. Apart from the electric force, no forces act on the particles. Rank them in order of the par» _ ' ticle’s change in kinetic energy, from largest to smallest. Rank increases (positive changes) higher than decreases (negative changes). (a)m=5 x10'”g.q= —5 nC. Vi: 100V, V{= —50V '-' (b) m = I X 10"Is g, q = —5 nC. V. = —50 V, V; = 50V (c) m = t x 10"5g. q = 25 no, v. = 50 v, V. = 20v (d) m = 5 x10'”g,q= —1nc.vi =400v. Vf- —100v (e)m=25 x10"5g.q=lnC,l/i= —100v, vr=—50v mm=1x|0-”g.q= 5nc, vi = 100v. vr= 250v An electron beam is deflected upward through 3.0 mm while traveling in a vacuum between two deflection plates 12.0 mm apart. The potential difference between ' the deflecting plates is 100.0 kV. and the kinetic energy ofeach electron as it enters the space between the plates is 2.0 x 10‘‘5 .I. What is the kinetic energy of each elec- tron when it leaves the space between the plates? $ EIMWM: 311mm . In the electron gun of Example 17.8. if the potential difference between the cathode and anode is reduced to 6.0 kV. with vt hat speed will the electrons reach the anode? . In the electron gun of Example 17.8, if the electrons reach the anode with a speed of 3.0 x 10"I this. what :_ is the potential difference between the cathode and the .' anode? . An electron (charge -e) is projected horizontally into the space between twu oppositely charged parallel -‘ plates. The electric field between the plates is 500.0 NIC upward. 1f the vertical deflection of the electron as it - leaves the plates has magnitude 3.0 mm. how much has its kinetic energy increased due to the electric field? [Hint First find the potential difference through which the electron moves] 1.54. An alpha particle (charge +29) moves through a poten- _‘-" tial difference AV = -—0.50 kV. Its initial kinetic energy is L20 x 10"" J. What is its final kinetic energy? 55. In I91 1. Ernest Rutherford discovered the nucleus of the atom by observing the scattering of helium nuclei from gold nuclei. If a helium nucleus with a mass of 6.68 x 10”” kg. a charge of +2e. and an initial veloc- ity of 1.50 x l0.Ir mils is projected head-on toward a gold nucleus with a charge of +79e. how close will the helium atom come to the gold nucleus before it stops and turns around? (Assume the gold nucleus is held in place by other gold atoms and does not move.) The figure shows a graph of electric potential versus position along the .r-axis. A proton is originally at point A, moving in the positive .r-direction. How much kinetic energy does it need to have at point A in order to be able to reach point E (with no forces acting on the proton other than those due to the indicated potential)? Points B. C , and D have to be passed on the way. Repeat Problem 56 for an electron rather than a proton . " n «: 150.0 v t A “00.0 \‘i E (55.0 V) l-F—I— Ci—stin vi Problems 56 and 57 $“'. 17.5 Capacitors ['58. A 2.0 pF capacitor is connected to a 9.0 V battery. What is the magnitude of the charge on each plate? I 59. The plates of a 15.0 pF capacitor have net charges of +0.75 pC and —0.75 ttC. respectively. (a) What is the potential difference between the plates? lb) Which plate is at the higher potential? If a capacitor has a capacitance of l0.2 11F and we al wish to lower the potential difference across the plates Ed by 60.0 V, what magnitude of charge will we have to remove from each plate? bl. A parallel plate capacitor has a capacitance of 2.0 11F and n5 plate separation of 1.0 mm. (a) How much potential differ- I'dl ence can be placed across the capacitor before dielectric he breakdown of air occurs (5.... = 3 x 10" Wm)? (b) \Vhat is the magnitude of the greatest charge the capacitor can llU store before breakdown? lel . 62. A parallel plate capacitor has plates of area 1.00 cm1 IC separated by 0.250 mm. There is a charge of magnitude '- il 4.00 pC on each plate. (it) Find the potential difference and the electric field between the plates. (b) if the plate separation is doubled while the charge is kept constant. what will happen to the potential difference and the electric field? PROBLEMS 651 63. A parallel plate capacitor has plates of area 36.0 cm2 separated by 0.0500 mm. The capacitor is connected to a 1.2 V battery. (a) Find the electric field between the plates and the magnitude of the charge on each plate. (b) If the plate separation is doubled while the plates remain connected to the battery, what happens to the electric field and the charge on each plate? 64. A variable capacitor is made of two paral- lel semicircular plates with air between them. One plate is fixed in place and the other can be rotated. The electric field is zero everywhere except in the region where the plates overlap. Wh...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern