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 y distnce d. The Coulom force etween them hs mgnitude F. After the chrges re pulled prt to lrger distnce, the mgnitude of the Coulom force is now F/4. Wht is the new distnce? [A] 4d [B] 2d [C] 16d [D] cnnot tell without knowing 1 nd 2 2. An electron is initilly trveling horizontlly with velocity v 0 in region where there is uniform electric field. The electric field deflects the electron down. Wht is the direction of the electric field? [A] up [B] down [C] right [D] left v 0. The electric potentil in some region of spce is given y V = Ax 2 y 2 By where A nd B re positive constnts. The y-component of the electric field is: [A] 2Axy 2 [B] 2Ax 2 y B [C] By [D] 2Axy 2 [E] 2Ax 2 y + B 4. An electric dipole plced in uniform electric field hs minimum electric potentil energy when p is nd mximum mgnitude torque when p is. [A] prllel to E, prllel to E. [B] prllel to E, perpendiculr to E. [C] perpendiculr to E, prllel to E. [D] perpendiculr to E, perpendiculr to E. 5. The cpcitnce of prllel-plte cpcitor cn e incresed y [A] decresing the chrge on ech plte [B] decresing the re of ech plte [C] decresing the spcing etween the pltes [D] decresing the potentil difference cross the pltes. /40 for pge 1
6. (40 points totl) A solid insulting sphere of rdius hs totl chrge distriuted uniformly throughout the sphere nd is surrounded y sphericl metl conducting shell of inner rdius nd outer rdius tht crries net chrge of. ) Use Guss Lw to derive n expression for the mgnitude of the electric field inside the insulting sphere for 0 < r <. (20 points) ) Wht is the electric field for < r <? (5 points) c) Using Guss Lw find the mgnitude of the electric field for r >. (10 points) d) Determine the chrge on the outer surfce of the sphericl metl conducting shell. (5 points) /40 for pge 2
7. (40 points totl) Three identicl positive point chrges sit on three of the corners of rectngle with edges of length nd s shown. y ) Determine the x nd y components of the electric field t the origin due to these three chrges. Express your nswer in terms of,,, nd Coulom s constnt k, ll of which you should leve in symolic form. (20 points) x ) Determine the electricl potentil t the origin due to these three point chrges, ssuming tht the potentil is zero t point infinitely fr wy. Express your nswer in terms of,,, nd Coulom s constnt k, ll of which you should leve in symolic form. (10 points) c) A proton is now plced t the origin. Determine the electricl force exerted on the proton y the three chrges. Express your nswer in unit vector nottion in terms of,,, Coulom s constnt k, nd the fundmentl electronic chrge e, ll of which you should leve in symolic form. (10 points) /40 for pge
8. (40 points totl) Positive electric chrge q 1 = +2 nd negtive chrges q 2 =, nd q = 10 re uniformly distriuted, respectively, long three insulting rods ent into qurter circles s shown in the figure. y q ) Clculte the net electric potentil t the origin due to the three ent chrged rods. (20 points) q 1 q 2-2 - 4 x ) A smll ll of mss m nd negtive chrge q is now slowly moved from infinity to the origin. How much work is done y the externl gent tht moves the chrge? (10 points) c) The smll ll of mss m nd negtive chrge q is now relesed from rest t the origin. Wht is the mximum speed it reches? (10 points) /40 for pge 4
9. (40 points totl) In the figure, C 1 = 4µ F, C 2 = 8µ F, C = 4µ F, nd C 4 = 2µ F. The cpcitor network is connected cross n pplied voltge V. After the chrges on the cpcitors hve reched their finl vlues, the chrge on C is = 192 µ C. ) Wht is the equivlent cpcitnce of the system? (10 points) C 1 C 2 C C 4 ) Wht re 4 nd V 4? (10 points) c) Wht re 1 nd V 1? (10 points) d) Wht re 2 nd V 2? (10 points) /40 for pge 5