Physics 24 Exam 1 February 18, 2014

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Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing through Gussin surfce is found to be positive.

1 Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing through Gussin surfce is found to be positive. Which of the following sttements must be true? [A] The totl chrge outside the surfce is positive. [B] The totl chrge inside the surfce is positive. [C] The totl chrge outside the surfce is negtive. [D] The totl chrge inside the surfce is negtive. 2. The figure shows n electric dipole with its dipole moment oriented perpendiculr to uniform electric field. For this orienttion the mgnitude of the torque on the dipole is nd the potentil energy of the dipole is. [A] 0, minimum [B] 0, mximum [C] minimum, 0 [D] mximum, E 3. A proton is relesed from rest in uniform electric field. The proton then moves under the influence of the electric field. Which of the following is true for the proton? [A] The proton s potentil energy increses nd it moves towrd higher electric potentil. [B] The proton s potentil energy decreses nd it moves towrd higher electric potentil. [C] The proton s potentil energy increses nd it moves towrd lower electric potentil. [D] The proton s potentil energy decreses nd it moves towrd lower electric potentil. 4. A prllel plte cpcitor with cpcitnce C 0 is connected to bttery of potentil V 0 nd cquires chrge Q 0. With the bttery still connected, the seprtion between the pltes is decresed by fctor of 2. Wht re the new chrge on the pltes nd potentil difference between them fter this chnge is mde? [A] 2Q 0, V 0 [B] Q 0 /2, V 0 [C] Q 0, 2V 0 [D] Q 0, V 0 /2 5. The Hoverdog in the picture is negtively chrged, nd the rings positively chrged. If the Hoverdog is relesed from rest, it will [A] Oscillte bck nd forth between the rings. [B] Lunch to the right t high speed. [C] Lick the nerest humn s fce. [D] Ask Dr. Prris, he s the Hoverdog expert. Note: no Hoverdogs were hrmed in the preprtion of this exm. /40 for pge 1

2 6. (40 points totl) A positive chrge Q is uniformly distributed over one hlf of semi-circle of rdius. Negtive chrge of twice tht mgnitude is uniformly distributed over the bottom hlf of the semi-circle, s shown in the figure. y () (5 points) Drw on the figure t right the individul electric fields due to the positive nd the negtively chrged hlves of the semi-circle. q 1 = +Q (b) (20 points) Clculte the electric field t the origin due to the positively chrged hlf of the semicircle, using the coordinte system indicted. Express your nswer in unit vector nottion, in terms of the prmeters Q,, nd Coulomb s constnt k. q 2 = -2Q O x (c) (15 points) Find the totl electric field t the origin, due to the entire semi-circle of chrge. Feel free to stte nd use ny pproprite symmetry rguments to simplify your clcultion. Express your nswer in unit vector nottion, in terms of the prmeters Q,, nd Coulomb s constnt k. /40 for pge 2

3 7. (40 points totl) A metl sphericl shell of inner rdius nd outer rdius b holds net positive chrge of +2Q. Inside this sphericl shell, held fixed t the center, is negtive point chrge Q. () (10 points) Strting from sttement of Guss s Lw, find the mgnitude of the electric field for r<. 2Q -Q b (b) (5 points) Wht is the mgnitude of the electric field for <r<b? (c) (10 points) Strting from sttement of Guss s Lw, find the mgnitude of the electric field for r>b. (d) (10 points) Find the surfce chrge densities σ nd σ b on the inner nd outer surfces of the conductor. (e) (5 points) Wht re the directions of E for r< nd r>b? You cn show the directions in digrm or describe the directions in words. /40 for pge 3

4 8. (40 points totl) You re building Coulomb gun, tht is, device tht uses the Coulomb force to fire bullet. Initilly, two identicl chrged spheres of rdius R nd mss m re held in plce inside n insulting frictionless brrel of length L (where L is defined in the figure). They re seprted by thin insulting brrier nd crry identicl positive chrges. When the trigger of the gun is pulled, the right sphere is relesed from rest. + + L () (20 points) Clculte the vlue Q of the spheres chrges such tht the bullet (the right sphere) hs speed v when its center reches the end of the brrel. You cn tret the chrges s point chrges t the centers of their respective spheres. (b) (10 points) Find the work done by the Coulomb force during the ccelertion of the bullet inside the brrel. (c) (10 points) Determine the mgnitude of the force required to hold the bullet in plce before the trigger is pulled. /40 for pge 4

5 9. (40 points totl) In the cpcitor circuit shown, V b - V = +30 volts. Use strting equtions for ll clcultions. () (15 points) Clculte the totl (equivlent) cpcitnce of this configurtion of cpcitors. C 3 = 3 µf C 1 = 6 µf C 2 = 12 µf c C 4 = 3 µf b (b) (15 points) Clculte the chrge stored in ech of the 3 microfrd cpcitors (C 3 nd C 4 ). (c) (10 points) Clculte the mgnitude of the potentil difference between points nd c. Which point is t higher potentil, or c? /40 for pge 5

Physics 2135 Exam 1 February 14, 2017

Physics 2135 Exam 1 February 14, 2017 Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted