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1999 PHYSICS C SECTION II, ELECTICITY AND MAGNETISM Time 45 minutes 3 Questions Directions: Answer ll three questions. The suggested time is bout 15 minutes for nswering ech of the questions, which re worth 15 points ech. The prts within question my not hve equl weight. Show ll your work in the pink booklet in the spces provided fter ech prt, NOT in this green insert. E&M 1. An isolted conducting sphere of rdius 020. m is t potentil of 2, 000V. () Determine the chrge Q 0 on the sphere. b r c The chrged sphere is then concentriclly surrounded by two unchrged conducting hemispheres of inner rdius b 040. m nd outer rdius c 050. m, which re joined together s shown bove, forming sphericl cpcitor. A wire is connected from the outer sphere to ground, nd then removed. (b) (d) Determine the mgnitude of the electric field in the following regions s function of the distnce r from the center of the inner sphere. i. r < ii. < r < b iii. b < r < c iv. r > c Determine the mgnitude of the potentil difference between the sphere nd the conducting shell. Determine the cpcitnce of the sphericl cpcitor.
B (out of pge) P O r E&M 2. A uniform mgnetic field B exists in region of spce defined by circle of rdius 060. m s shown bove. The mgnetic field is perpendiculr to the pge nd increses out of the pge t constnt rte of 040. T/s. A single circulr loop of wire of negligible resistnce nd rdius r 090. m is connected to lightbulb with resistnce 50. 9, nd the ssembly is plced concentriclly round the region of mgnetic field. () (b) Determine the emf induced in the loop. Determine the mgnitude of the current in the circuit. On the figure bove, indicte the direction of the current in the loop t point O. Determine the totl energy dissipted in the lightbulb during 15 s intervl. b The experiment is repeted with loop of rdius b 040. m plced concentriclly in the sme mgnetic field s before. The sme lightbulb is connected to the loop, nd the mgnetic field gin increses out of the pge t rte of 040. T/s. Neglect ny direct effects of the field on the lightbulb itself. (d) Stte whether the brightness of the bulb will be greter thn, less thn, or equl to the brightness of the bulb in prt (). Justify your nswer.
y Q z x E&M 3. The nonconducting ring of rdius shown bove lies in the yz-plne nd crries uniformly distributed positive chrge Q. () Determine the electric potentil t points long the x-xis s function of x. (b) i. Show tht the x-component of the electric field long the x-xis is given by Qx Ex =. 3 2 2 2 4 π ( + x ) 0 ii. Wht re the y- nd z- components of the electric field long the x-xis? Determine the following. i. The vlue of x for which E x is mximum ii. The mximum electric field E x mx
(d) On the xes below, sketch E x versus x for points on the x-xis from x = 2 to x = +2. E x 2 2 x (e) An electron is plced t x = /2 nd relesed from rest. Qulittively describe its subsequent motion. S T O P END OF SECTION II, ELECTICITY AND MAGNETISM