Exm Totl Physics 2135 Exm 1 September 23, 2014 Key Printe Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. B 1. Object A hs chrge of +2 µc n object B hs chrge of +4 µc. If F A is the force exerte on object A by object B, n F B is the force on B by A which of the following is true? [A] FA = 2FB [B] FA = FB [C] 2F A = F B [D] FA = 2FB B 2. An electric ipole plce in uniform electric fiel hs mximum electric potentil energy when p is to E. [A] prllel [B] ntiprllel [C] perpeniculr [D] ntiperpeniculr A 3. Ienticl positive point chrges re plce t two of the vertices of n equilterl tringle, s shown. Point P is t the thir vertex. Wht chrge must be plce t point P so tht the electric potentil t the center of the tringle, istnce from ech of the vertices, is zero? [A] -2Q [B] +2Q [C] Q/2 [D] Q P D 4. A prllel plte cpcitor with cpcitnce C 0 is connecte to bttery of potentil V 0 n cquires chrge Q 0. The cpcitor is then isconnecte from the bttery. After the cpcitor hs been isconnecte, the seprtion between the pltes is ecrese by fctor of 2. Wht re the new chrge on the pltes n potentil ifference between them fter this chnge is me? [A] 2Q 0, V 0 [B] Q 0 /2, V 0 [C] Q 0, 2V 0 [D] Q 0, V 0 /2 ABCD 5. Wht is wrong with this picture of Hoverog? [A] Everyboy knows Hoverogs on t exist. [B] Everyboy knows Hoverogs cn t trvel t supersonic spees. [C] At tht spee the grss behin the Hoverogs shoul be flttene by its wke turbulence. [D] Nothing. Spee: 1500 km 40 /40 for pge 1
y 6. (40 points totl) Consier the chrge istribution shown. A semicircle of rius centere t the origin crries uniform positive chrge per unit length λ. Two positive point chrges Q lie t the points (-,) n (,). You my use symmetry rguments when pproprite. Q Q () (20 points) Fin n expression for the electric fiel t the origin ue to the chrge semicircle only. Express your nswer in unit vector nottion. x (b) (15 points) Fin n expression for the electric fiel t the origin ue to the point chrges only. Express your nswer in unit vector nottion. (c) (5 points) Fin the vlue of Q for which the electric fiel t the origin is zero. /40 for pge 2
7. (40 points totl) A soli insulting plstic sphere of rius crries totl net positive chrge 3Q uniformly istribute throughout its interior. The insulting sphere is cote with metllic lyer of inner rius n outer rius 2. The conucting metllic lyer crries net chrge of -2Q. () (10 points) Compute the volume chrge ensity ρ ssocite with the chrge uniformly istribute in the plstic sphere in terms of vribles introuce bove. 2 (b) (10 points) Apply Guss s lw to fin the mgnitue of the electric fiel in the region r <. In the figure, rw the Gussin surfce you re using, n inicte on tht surfce the irection of ny vectors which pper in the mthemticl expression of Guss s lw. Express your nswer in terms of, Q, r, n ε 0. (If you get n expression involving ρ, substitute it from bove to re-express your nswer in terms of the stte vribles.) (c) (10points) Fin the electric fiel in the region < r < 2. Justify your nswer. () (10 points) Fin the net chrge q i resiing on the inner surfce of the metllic lyer, n the net chrge q o resiing on the outer surfce of the metllic lyer. /40 for pge 3
8. (40 points totl) An irregulrly shpe uniform chrge istribution with totl chrge is shown below. An electron (with chrge e) strts from rest t point A n moves to point B. The electrosttic potentil t A is V A, n the electrosttic potentil t B is V B.. () (10 points) Using only the prmeters given bove n beginning with n officil strting eqution, fin the work one by the electric fiel s the electron moves from point A to point B. B uniform chrge istribution A (b) (10 points) Is the work one by the electric fiel s the electron moves from A to B positive, negtive, or zero? (circle one) POSITIVE NEGATIVE ZERO (c) (20 points) Fin the mgnitue of the potentil ifference between the points A n B if the spee of the electron t B is 4.2 x 10 5 m/s. Begin with n OSE n erive the finl expression use to clculte the potentil ifference. /40 for pge 4
9. (40 points totl) Four cpcitors re connecte s shown. C 1 = 5 µf, C 2 = 3 µf, C 3 = 6 µf, n C 4 = 3 µf. The voltge ifference cross the cpcitor network is V b = 60 V. () (20 points) Determine the equivlent cpcitnce of the cpcitor network. C 1 = 5 µf C 2 = 3 µf C 4 = 3 µf C 3 = 6 µf b (b) (10 points) Determine the chrge Q 1 on cpcitor C 1. (c) (10 points) Determine the chrge Q 4 on cpcitor C 4. /40 for pge 5