- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.

Transcription

1 - 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked.

2 - 6 - QUESTION 1 [Mrks 22] A thin non-conducting rod of length L hs chrge q uniformly distributed long its length s shown in the digrm (i). (i) q L P () Determine the liner chrge density on the rod. Determine the vlue of the electric field (intensity) E (mgnitude nd direction) t the point P s shown in the digrm, distnce from the end of the rod. (c) For the configurtion shown in the digrm (ii), determine the vlue of the electric field (intensity) E (mgnitude nd direction) t the point P. You my use your result from prt. (ii) q L P q L

3 - 7 - QUESTION 2 [Mrks 21] # 1 Three points in spce re lbelled #1, #2 nd #3 nd their positions re shown on the digrm. The points form right-ngled tringle with dimensions s shown. Initilly there is no electric field in spce. # 2 # 3 () (c) (d) (e) (f) Clculte the work required (by n externl gent) to plce chrge of +3q t position #1, if it is initilly infinitely fr from position #1. With +3q t position #1, clculte the work required (by n externl gent) to plce chrge of 2q t position #2, if it is initilly infinitely fr from the chrge now t position #1. With +3q t position #1, nd 2q t position #2, clculte the work required (by n externl gent) to plce chrge +q t position #3, if it is initilly infinitely fr from the chrges, which re now t positions #1 nd #2. Clculte the electric potentil energy of the chrge +q t position #3 with respect to infinity in the presence of the other chrges now t the positions #1 nd #2. Clculte the totl work required (by n externl gent) to ssemble ll three chrges from their initil positions to their finl positions s detiled in prts (), nd (c). Determine the electric potentil energy of the system of three chrges when ll re in their finl positions s detiled in prts (), nd (c).

4 - 8 - QUESTION 3 [Mrks 29] An electron is ccelerted from rest through potentil difference of 1.0 kv nd directed into region between two prllel metl pltes seprted by 20 mm with potentil difference of 100 V between them. The prllel pltes re thin nd very lrge compred to the seprtion between them nd ech plte hs the sme mgnitude of surfce chrge density on it. () Determine the velocity of the electron before it enters the prllel pltes. Determine the mgnitude of the electric field (intensity) E between the prllel pltes. The electron now enters the region between the prllel pltes moving perpendiculr to the electric field between them. (c) Drw cler digrm showing the prllel pltes, the direction of the electric field nd the velocity vector of the electron on entering the pltes. A mgnetic field is lso pplied between the prllel pltes. (d) (e) (f) Determine the mgnetic field (induction) B (mgnitude nd direction) which is perpendiculr to both the electron pth nd the electric field, such tht the electron will trvel in stright line. Neglect the grvittionl force on the electron. Show the direction of B from prt (d) on your digrm in prt (c). Use the Guss Lw to determine the numericl vlue of the surfce chrge density on the prllel pltes. You must show ll working including the Gussin surfce tht you choose.

5 - 9 - QUESTION 4 [Mrks 28] () Stte the Biot-Svrt Lw for mgnetosttics nd if you use symbols, crefully explin the mening of ech symbol. The digrm shows circuit with curved segments tht re prts of circles of rdii nd b. The stright segments re long the rdii. A current i flows in the circuit. Determine the mgnetic field (induction) B (mgnitude nd direction) t the point P in terms of the given quntities in the digrm. i b θ P (c) (d) (e) Stte the Frdy Lw of electromgnetic induction nd if you use symbols, crefully explin the mening of ech symbol. Using br mgnet nd loop of wire, describe in words nd with the id of digrms, how you could physiclly demonstrte the electromgnetic induction effect. Apply the Frdy Lw to give detiled explntion of why the electromgnetic induction effect occurs in the demonstrtion you described in prt (d).

6 TEST 1R This is the repet version of TEST 1, which ws held during Session. This repet test should be ttempted by those students who missed Test 1, or who wish to improve their mrk in Test 1. IF YOU ARE ATTEMPTING TEST 1 (Repet): CROSS THIS BOX AND INDICATE YES ON THE FRONT (TITLE) PAGE.

7 QUESTION 5 [Mrks 25] y () A prticle executes uniform circulr motion with rdius r, s shown in the figure. (i) From the figure, derive n expression for the position vector r in terms of the rdius r, the ngulr velocity ω, the time t, nd unit vectors i r nd r j. Tke the ngle t time t = 0 to be zero. r ωt x (ii) From (i), derive the velocity v r nd ccelertion r of the prticle. Express the result for the ccelertion in terms of the position vector. (iii) Clculte the sclr product of the velocity nd position vectors, v r " r. Wht does this sy bout the reltive orienttion of v r nd r? A stone is tied to string nd swings with uniform motion in horizontl circle. The string r r r r r breks nd t time t 1 lter, the stone is displced! = (5.5i + 7.9j! 3.1k) metres. (The positive z-xis is verticlly up.) r 1 (i) Find time t 1. (ii) Wht ws the speed of the stone while in circulr motion?

8 QUESTION 6 [Mrks 26] A smll block of mss m=254g slides long trck s shown in the figure. The left side of the trck is elevted nd hs frictionless surfce. From x==35.0cm, the surfce is rough nd flt, with length L=2.37m. At the fr right, t x=l+, is spring with spring constnt k=4.36n/cm bove frictionless surfce of length =35.0cm. In trversing the flt prt of the trck (through distnce L), 728mJ of mechnicl energy is lost due to friction. The block is relesed from height h=95.0cm bove the flt prt of the trck. h k x = 0 L x = x = L + x = L + 2 () For the first return trip to the incline, clculte: (i) the speed of the block t x= (on first pproch to the rough surfce); (ii) the mximum compression of the spring; (iii) the mximum height on return to the incline. Find the position where the block comes to rest on the rough flt surfce.

9 QUESTION 7 [Mrks 19] The Sun, mss m= kg, revolves round the centre of the Milky Wy glxy, distnce R= m wy. The Sun completes one revolution every yers. () (c) Clculte the tngentil speed v of the Sun bout the glctic centre. From Newton's second lw nd Newton's lw of grvittion, derive n expression for the mss of the glxy M in terms of the Sun's tngentil speed v, the grvittionl constnt G, nd the distnce R. (Assume tht the mss of the glxy is distributed with sphericl symmetry bout its centre nd tht the Sun is t the glctic edge.) Hence, estimte the number of strs in the Milky Wy. (Assume the mss of the glxy M is comprised entirely of strs nd tht the mss of the Sun is typicl for str.)

10 QUESTION 8 [Mrks 30] () A 104g copper ring hs dimeter of cm t its temperture of 0 degrees Celsius. An luminium sphere hs dimeter of cm t its temperture of 100 degrees Celsius. The sphere is plced on top of the ring, nd the two re llowed to come to therml equilibrium, no het being lost to the surroundings. The sphere just psses through the ring t the equilibrium temperture. (i) (ii) Wht is the equilibrium temperture? Wht is the mss of the sphere? Coefficients for liner expnsion - Copper: α = 17 x 10-6 K -1 ; Aluminium: α = 23 x 10-6 K -1 Specific het cpcities - Copper: c = 387 J/(kg.K); Aluminium: c = 900 J/(kg.K) A quntity of idel gs occupies n initil volume V 0 t pressure P 0 nd temperture T 0. The gs expnds to volume V 1. [Cutionry note: in nswering questions (ii)-(iv), py ttention to signs. E.g., -5 is less thn -4.] (i) (ii) On PV digrm, grph the expnsion for three cses: (1) constnt pressure (isobric expnsion), (2) constnt temperture (isotherml expnsion), (3) no het exchnge (dibtic expnsion). In which cse is the work done on the gs the gretest? The lest? Present ll resoning/working. (iii) In which cse is the het dded to the gs the gretest? The lest? Present ll resoning/working. (iv) In which cse is the chnge in internl energy "E int the gretest? The lest? Present ll resoning/working.