PHS 212 Midterm 2 with Solution, Spring 2004

NDU PHS 212 - Electricity & Magnetism Faculty of Natural and Applied Sciences Midterm Exam II - Department of Sciences Duration: 100 minutes (1h40) 1. (5-G.7)An insulating disk of radius a is centered at the origin with its normal along the x-axis. It is given a charge density o=Br . p> a. Find its total charge Q. b. Find the potential Vx) along the x-axis. c. Verify that V(x) has the expected behavior at large x. 2 2. (5-6.5) In the quark model, a proton consists of two “up” u quarks, each of charge 3° , anda 1 “down” d quark, of charge 3° . If they form an equilateral triangle of side a=107°m find a. the potential at one of the up quarks due to the other 2 quarks, b. the potential at the down quark due to the 2 up quarks, and c. the total energy of all the quarks. 3. (6-7.1) A parallel-plate capacitor is charged up by a 6V battery, which is then removed. A dielectric with dielectric constant x=5 is slid between the plates. Give quantitative answers in terms of the ratio of each quantity before and after. a) What happens to the electric field within the dielectric? b) What happens to the voltage difference between fhe plates? c) What happens to the charge on tt the plates?-d) ‘What-happens to the capacitance? e) What happen§ é fo the energy stored? Ex _- “emlergy is conserved, va ~ z ee - 7 “nH. 4. (10-4.14) A loop of radius a, carrying current J counterclockwise as seen from +x, is in a magnetic field B whose magnitude B is fixed, but whose direction always makes a flaring angle @ away from the axis of the loop. Draw and evaluate the force dF onanelement a that is-at the top of the loop. Find the component of d F along the x-axis. Integrate to obtain the total force on the loop. Why is it only along the x-axis? 5. (10-6.4) An electron beam with a kinetic energy of 8 keV ( LkeV =1000eV=1.6x10"'% ) moves in a circle of radius 2.4 cm. Find a. its velocity, 4 Ks We b. the period of the motion, Mh » c, the magnitude of the magnetic field it is in, ‘ g pom d. the magnetic force, and ys <) mn e. the radial acceleration. Ww og W> Q m,=9.11 X10 kg ;e=1.602X10°"C —_s s NOTRE DAME UNIVERSITY Zouk Moshbech - Leianon Name 2... eemcecunccnnesee, OD: RS Course NO eSectows. ans 1 | a a ee eee ee ee Hedited® VEEL TEE en Te : | ler i PIP TERETE HH} i: whi]? se :¥ . ao . mS iT] : feel] ee S| Y|\ it tite] ig (ice ia iffe H to ‘ “ee as heen 4 : lle all : ol, TLL (E2 Eb sda FEL RTE! ; ee en ul * fal ea Heras eed { : i WE Tn Tet Folds () — ns faz! el - 1‘ ee ee i | r es | i { come Lard < ONAN AA. AH) ei | —<] ro! > : ! aa ~ i ., NW): ea) Th 5 r ky i = 4 + sb jenn a. S So, ate ae Seis ! <J ve on i ver, | = - - =| \ 2GTRE DAME UNIVERSITY Zouk Moshek - Lebanon Name»... LULA Course N° (al singel al ; | | . a = pecan | ; in a Ft | 7 p aol = — | Ma i T Hsaies == = = yoke =< ~ BIN ! x : SE be ts = AL Le=—HS e a i = =e rp ai i =F = tt [= | WC = i tI Pa RA [py :, = E " Zt A \ I Ee 5 =a = 4 £’ A = riew io =H ashe Ea & = : eh P oe ‘i ; BB ) 70 aE == pf A a a i 22S ‘a pI r—h “OF 1 a’ ¥, AIDA = N i ¥ y i— Li} I HN ie va t/ hs ¢ Be 1 NS | PS S ++ — =H TERETE UPET EU ET TEEPE EEN dad ~ : - -— -— pantie att] ] == Sf pee fe pe - <= aan = on eel ne SE ENS PSN ,