Chapte 23: GAUSS LAW 1 A total chage of 63 10 8 C is distibuted unifomly thoughout a 27-cm adius sphee The volume chage density is: A 37 10 7 C/m 3 B 69 10 6 C/m 3 C 69 10 6 C/m 2 D 25 10 4 C/m 3 76 10 4 C/m 3 ans: 2 Chage is placed on the suface of a 27-cm adius isolated conducting sphee The suface chage density is unifom and has the value 69 10 6 C/m 2 The total chage on the sphee is: A 56 10 10 C B 21 10 8 C C 47 10 8 C D 63 10 8 C 95 10 3 C 3 A spheical shell has an inne adius of 37 cm and an oute adius of 45 cm If chage is distibuted unifomly thoughout the shell with a volume density of 61 10 4 C/m 3 the total chage is: A 10 10 7 C B 13 10 7 C C 20 10 7 C D 23 10 7 C 40 10 7 C ans: A 4 A cylinde has a adius of 21 cm and a length of 88 cm Total chage 61 10 7 C is distibuted unifomly thoughout The volume chage density is: A 53 10 5 C/m 3 B 53 10 5 C/m 2 C 85 10 4 C/m 3 D 50 10 3 C/m 3 63 10 2 C/m 3 Chapte 23: GAUSS LAW 343
5 When a piece of pape is held with one face pependicula to a unifom electic field the flux though it is 25 N m 2 /C When the pape is tuned 25 with espect to the field the flux though it is: B 12 N m 2 /C C 21 N m 2 /C D 23 N m 2 /C 25 N m 2 /C 6 The flux of the electic field (24 N/C) î + (30 N/C) ĵ + (16 N/C) ˆk though a 20m 2 potion of the yz plane is: A 32 N m 2 /C B 34 N m 2 /C C 42 N m 2 /C D 48 N m 2 /C 60 N m 2 /C 7 Conside Gauss s law: da = q/ 0 Which of the following is tue? A must be the electic field due to the enclosed chage B If q = 0, then = 0 eveywhee on the Gaussian suface C If the thee paticles inside have chages of +q, +q, and 2q, then the integal is zeo D on the suface is eveywhee paallel to da If a chage is placed outside the suface, then it cannot affect at any point on the suface 8 A chaged point paticle is placed at the cente of a spheical Gaussian suface The electic flux Φ is changed if: A the sphee is eplaced by a cube of the same volume B the sphee is eplaced by a cube of one-tenth the volume C the point chage is moved off cente (but still inside the oiginal sphee) D the point chage is moved to just outside the sphee a second point chage is placed just outside the sphee 9 Choose the INCOCT statement: A Gauss law can be deived fom Coulomb s law B Gauss law states that the net numbe of lines cossing any closed suface in an outwad diection is popotional to the net chage enclosed within the suface C Coulomb s law can be deived fom Gauss law and symmety D Gauss law applies to a closed suface of any shape Accoding to Gauss law, if a closed suface encloses no chage, then the electic field must vanish eveywhee on the suface ans: 344 Chapte 23: GAUSS LAW
10 The oute suface of the cadboad cente of a pape towel oll: A is a possible Gaussian suface B cannot be a Gaussian suface because it encloses no chage C cannot be a Gaussian suface since it is an insulato D cannot be a Gaussian suface because it is not a closed suface none of the above 11 A physics instucto in an anteoom chages an electostatic geneato to 25 µc, then caies it into the lectue hall The net electic flux in N m 2 /C though the lectue hall walls is: B 25 10 6 C 22 10 5 D 28 10 6 can not tell unless the lectue hall dimensions ae given 12 A point paticle with chage q is placed inside the cube but not at its cente The electic flux though any one side of the cube: A is zeo B is q/ 0 C is q/4 0 D is q/6 0 cannot be computed using Gauss law ans: 13 A paticle with chage 50-µC is placed at the cone of a cube The total electic flux in N m 2 /C though all sides of the cube is: B 71 10 4 C 94 10 4 D 14 10 5 56 10 5 ans: 14 A point paticle with chage q is at the cente of a Gaussian suface in the fom of a cube The electic flux though any one face of the cube is: A q/ 0 B q/4π 0 C q/3 0 D q/6 0 q/12 0 Chapte 23: GAUSS LAW 345
15 The table below gives the electic flux in N m 2 /C though the ends and ound sufaces of fou Gaussian sufaces in the fom of cylindes ank the cylindes accoding to the chage inside, fom the most negative to the most positive A 1, 2, 3, 4 B 4, 3, 2, 1 C 3, 4, 2, 1 D 3, 1, 4, 2 4, 3, 1, 2 ans: left end ight end ounded suface cylinde 1: +2 10 9 +4 10 9 6 10 9 cylinde 2: +3 10 9 2 10 9 +6 10 9 cylinde 3: 2 10 9 5 10 9 +3 10 9 cylinde 4: +2 10 9 5 10 9 3 10 9 16 A conducting sphee of adius 001 m has a chage of 10 10 9 C deposited on it The magnitude of the electic field in N/C just outside the suface of the sphee is: B 450 C 900 D 4500 90, 000 17 A ound wastepape basket with a 015-m adius opening is in a unifom electic field of 300 N/C, pependicula to the opening The total flux though the sides and bottom, in N m 2 C, is: B 42 C 21 D 280 can not tell without knowing the aeas of the sides and bottom 18 10 C of chage ae placed on a spheical conducting shell A paticle with a chage of 3C is placed at the cente of the cavity The net chage on the inne suface of the shell is: A 7C B 3C C 0 C D +3 C +7 C 346 Chapte 23: GAUSS LAW
19 10 C of chage ae placed on a spheical conducting shell A paticle with a chage of 3C is placed at the cente of the cavity The net chage on the oute suface of the shell is: A 7C B 3C C 0 C D +3 C +7 C ans: 20 A 30-N/C unifom electic field points pependiculaly towad the left face of a lage neutal conducting sheet The suface chage density in C/m 2 on the left and ight faces, espectively, ae: A 27 10 9 C/m 2 ;+27 10 9 C/m 2 B +27 10 9 C/m 2 ; 27 10 9 C/m 2 C 53 10 9 C/m 2 ;+53 10 9 C/m 2 D +53 10 9 C/m 2 ; 53 10 9 C/m 2 0; 0 ans: A 21 A solid insulating sphee of adius contains positive chage that is distibuted with a volume chage density that does not depend on angle but does incease with distance fom the sphee cente Which of the gaphs below might give the magnitude of the electic field as a function of the distance fom the cente of the sphee? A B C D Chapte 23: GAUSS LAW 347
22 Which of the following gaphs epesents the magnitude of the electic field as a function of the distance fom the cente of a solid chaged conducting sphee of adius? A B C D ans: 23 Chage Q is distibuted unifomly thoughout an insulating sphee of adius The magnitude of the electic field at a point /2 fom the cente is: A Q/4π 0 2 B Q/π 0 2 C 3Q/4π 0 2 D Q/8π 0 2 none of these 24 Positive chage Q is distibuted unifomly thoughout an insulating sphee of adius, centeed at the oigin A paticle with positive chage Q is placed at x =2on the x axis The magnitude of the electic field at x = /2 on the x axis is: A Q/4π 0 2 B Q/8π 0 2 C Q/72π 0 2 D 17Q/72π 0 2 none of these 25 Chage Q is distibuted unifomly thoughout a spheical insulating shell The net electic flux in N m 2 /C though the inne suface of the shell is: B Q/ 0 C 2Q/ 0 D Q/4π 0 Q/2π 0 ans: A 348 Chapte 23: GAUSS LAW
26 Chage Q is distibuted unifomly thoughout a spheical insulating shell The net electic flux in N m 2 /C though the oute suface of the shell is: B Q/ 0 C 2Q/ 0 D Q/4 0 Q/2π 0 ans: B 27 A 35-cm adius hemisphee contains a total chage of 66 10 7 C The flux though the ounded potion of the suface is 98 10 4 N m 2 /C The flux though the flat base is: B +23 10 4 N m 2 /C C 23 10 4 N m 2 /C D 98 10 4 N m 2 /C +98 10 4 N m 2 /C 28 Chage is distibuted unifomly along a long staight wie The electic field 2 cm fom the wie is 20 N/C The electic field 4 cm fom the wie is: A 120 N/C B 80 N/C C 40 N/C D 10 N/C 5 N/C 29 Positive chage Q is placed on a conducting spheical shell with inne adius 1 and oute adius 2 A paticle with chage q is placed at the cente of the cavity The magnitude of the electic field at a point in the cavity, a distance fom the cente, is: A zeo B Q/4π 0 1 2 C q/4π 0 2 D (q + Q)/4π 0 2 (q + Q)/4π 0 (1 2 2 ) 30 Positive chage Q is placed on a conducting spheical shell with inne adius 1 and oute adius 2 A point chage q is placed at the cente of the cavity The magnitude of the electic field at a point outside the shell, a distance fom the cente, is: A zeo B Q/4π 0 2 C q/4π 0 2 D (q + Q)/4π 0 2 (q + Q)/4π 0 (1 2 2 ) Chapte 23: GAUSS LAW 349
31 Positive chage Q is placed on a conducting spheical shell with inne adius 1 and oute adius 2 A point chage q is placed at the cente of the cavity The magnitude of the electic field poduced by the chage on the inne suface at a point in the inteio of the conducto, a distance fom the cente, is: B Q/4vπ 0 1 2 C Q/4π 0 2 2 D q/4π 0 2 Q/4π 0 2 32 A long line of chage with λ chage pe unit length uns along the cylindical axis of a cylindical shell which caies a chage pe unit length of λ c The chage pe unit length on the inne and oute sufaces of the shell, espectively ae: A λ and λ c B λ and λ c + λ C λ and λ c λ c D λ + λ c and λ c λ λ λ c and λ c + λ ans: B 33 Chage is distibuted unifomly on the suface of a lage flat plate The electic field 2 cm fom the plate is 30 N/C The electic field 4 cm fom the plate is: A 120 N/C B 80 N/C C 30 N/C D 15 N/C 75N/C 34 Two lage insulating paallel plates cay chage of equal magnitude, one positive and the othe negative, that is distibuted unifomly ove thei inne sufaces ank the points 1 though 5 accoding to the magnitude of the electic field at the points, least to geatest A 1, 2, 3, 4, 5 B 2, then 1, 3, and 4 tied, then 5 C 1, 4, and 5 tie, then 2 and 3 tie D 2 and 3 tie, then 1 and 4 tie, then 5 2 and 3 tie, then 1, 4, and 5 tie + 1 + 23 4 5 350 Chapte 23: GAUSS LAW
35 Two lage paallel plates cay positive chage of equal magnitude that is distibuted unifomly ove thei inne sufaces ank the points 1 though 5 accoding to the magnitude of the electic field at the points, least to geatest A 1, 2, 3, 4, 5 B 5, 4, 3, 2, 1 C 1, 4, and 5 tie, then 2 and 3 tie D 2 and 3 tie, then 1 and 4 tie, then 5 2 and 3 tie, then 1, 4, and 5 tie ans: + + 1 + 23 + 4 5 36 A paticle with chage Q is placed outside a lage neutal conducting sheet At any point in the inteio of the sheet the electic field poduced by chages on the suface is diected: A towad the suface B away fom the suface C towad Q D away fom Q none of the above 37 A hollow conducto is positively chaged A small unchaged metal ball is loweed by a silk thead though a small opening in the top of the conducto and allowed to touch its inne suface Afte the ball is emoved, it will have: A a positive chage B a negative chage C no appeciable chage D a chage whose sign depends on what pat of the inne suface it touched a chage whose sign depends on whee the small hole is located in the conducto 38 A spheical conducting shell has chage Q A paticle with chage q is placed at the cente of the cavity The chage on the inne suface of the shell and the chage on the oute suface of the shell, espectively, ae:, Q B q, Q q C Q, 0 D q, Q + q q, 0 Chapte 23: GAUSS LAW 351