SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CONSTANTS

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Shona Owens
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1 Cicle instucto: Moow o Yethiaj Name: MEMORIL UNIVERSITY OF NEWFOUNDLND DEPRTMENT OF PHYSICS ND PHYSICL OCENOGRPHY Final Eam Phsics 5 Winte 3:-5: pil, INSTRUCTIONS:. Do all SIX (6) questions in section and all THREE (3) questions in section. Do TWO questions fom section 3. Maks ae indicated in the left magin. Section contains 36 maks, Section contains 36 maks, and section 3 contains 8 maks. udget time accodingl.. You ma use a calculato. ll othe aids ae pohibited. 3. Wite answes neatl in space povided. If necessa, continue onto the back of the page. 4. Do not ease o use whiteout. Daw a line neatl though mateial to be eplaced. 5. ssume all infomation given is accuate to 3 significant figues. 6. Don t panic. If something isn t clea, SK! SEE LST PGE FOR SOME POTENTILLY USEFUL FORMULE ND CONSTNTS Fo office use onl: TOTL

Cicle instucto: Moow o Yethiaj Name: SECTION : Thee ae 6 SHORT NSWER questions. Each is woth 6 maks fo a maimum of 36 maks. udget time accodingl. [6]. simple pendulum has a mass of.

2 Cicle instucto: Moow o Yethiaj Name: SECTION : Thee ae 6 SHORT NSWER questions. Each is woth 6 maks fo a maimum of 36 maks. udget time accodingl. [6]. simple pendulum has a mass of.5 kg and a length of.75 m. It is displaced though an angle 5 (.6 adians ) and then eleased. (a) What is the maimum tangential speed? (b) Obtain an epession fo the angula acceleation, d / dt, when the pendulum is at an abita angle, in adians, with espect to the vetical. [6]. C chage is at the cente of an unchaged (3-dimensional) insulating cubic shell with 5 cm edges. This shell, in tun, is cented inside of a metal (conducting) cubic shell with cm edges. conducting insulating (a) Find the electic flu though one face of the insulating cubic shell. (b) What is the total suface chage spead ove the entie inne suface of the conducting cubic shell? (c) The chage is moved slightl to the left so it emains within the insulating cubic shell but is no longe at the cente. Will this change ou answes fo (a), (b), both, o neithe. (Hint: No calculations ae needed fo this pat.)

3 Cicle instucto: Moow o Yethiaj 3 Name: - - [6] 3. (a) wave is descibed b the function, t).7 msin 8.4 m 75s what speed does this wave tavel? ( t. t (b) Waves with a wavelength of 638 nm ae incident on a baie with two small slits 6 sepaated b a distance d 5 m. The two paallel as point towad a spot on a distant sceen at which the waves fom the two slits intefee constuctivel. If that is the fist bight spot above the cente of the intefeence patten on the sceen, what is the angle? You d can assume that is small. [6] 4. The diagams show two aangements of polaies with tansmission aes oiented in diffeent diections in the - plane. In each case, unpolaied light taveling in the. diection fist passes though a polaie with its tansmission ais paallel to the diection and emeges with an intensit I. Subsequent polaies ae labeled b the angle between thei tansmission aes and the diection. Fo each aangement, calculate the intensit, in tems of I, of the light emeging fom the last polaie. 45 o I o. o C. I o 9 o I o D. 45 o 9 o I o

4 Cicle instucto: Moow o Yethiaj 4 Name: [6] 5. squae loop of wie is situated in a egion of unifom magnetic field with its diagonal paallel to the magnetic field lines as shown. cuent of. ciculates counteclockwise aound the loop. Each side of the squae is.7 m long. The ais sstem is as shown with the ais out of the page. The magnetic field is.5 T ˆj (a) What is the magnetic foce on the side ab? Give ou answe in unit vecto notation. (b) What is the magnetic moment,, of the loop? Give ou answe in unit vecto notation. (c) What is the toque,, on the loop? Give ou answe in unit vecto notation. [6] 6. Two glass plates (n =.45) ae touching along one edge and sepaated b a thin wie along the othe as shown. When the ae illuminated b monochomatic light, altenating dak and bight bands ae seen in eflection. (a) iefl eplain wh thee is a dak band, which we will call the st dak band, at the end whee the plates ae touching. (b) The net dak band (the nd ) is occus whee the plates ae sepaated b 39 nm. What is the wavelength of the light? (c) Imagine that the space between the plates is now filled with light oil having an inde of efaction n =.33. Does the spacing between adjacent bands incease o decease? iefl justif ou answe.

5 Cicle instucto: Moow o Yethiaj 5 Name: SECTION : Do LL thee (3) questions. Each question is woth maks fo a maimum of 36 maks. 9 [] 7. One point chage, q 3. C, is located 5 cm fom the oigin along the ais. second point chage, 9 q 5. C, is located 5 cm fom the oigin along the -ais as shown. (a) What is the foce on chage due to chage? Give ou answe in unit vecto notation. (b) What is the magnitude of the electic field at the oigin (point P)? (c) What is the electic potential at the oigin (point P)? (d) How much wok would be done b the electic field if chage wee moved fom the position shown to the oigin? (e sue to indicate the sign.)

6 Cicle instucto: Moow o Yethiaj 6 Name: [] 8. student who likes to do things the had wa wishes to measue the length, L T, of a tube that is open at one end and closed at the othe. He has a sting with a length L S =.4 m and a mass of.6 kg. He finds that the fundamental esonance of the sting matches one hamonic of the tube (not the fundamental) when the tension in the sting is 576 N. To match the net hamonic of the tube, he must incease the sting tension to 6 N. (a) What is the fundamental fequenc of the sting when its tension is 576 N? (b) What is the fundamental fequenc of the sting when its tension is 6 N? (c) ased on ou pevious answes, what is the fundamental fequenc of the tube? (Hint: Fo a tube closed at one end, how is the diffeence in fequenc between one hamonic and the net elated to the fundamental fequenc?) (d) What is the length of the tube? ssume that the speed of sound in ai is 343 m/s. (Hint: How is the length of the tube elated to the wavelength of the fundamental tube hamonic?)

7 Cicle instucto: Moow o Yethiaj 7 Name: [] 9. Two ve lage squae metal sheets with ae sepaated b 5. mm. Thee is a unifom electic field in the space between them and the potential diffeence between them is 5 V. =9.4 T (a) What is the magnitude of the electic field between the plates? 9 7 (b) n ion with a chage of 3. C and a mass of 6.6 kg is eleased fom est on the suface of the positive plate. What is its speed as it passes though a small hole on the negative plate? (c) fte it emeges fom the hole in the negative plate, the ion entes a egion of space containing a 9.4 T magnetic field oiented pependicula to its velocit. What is the magnitude of the magnetic foce on the ion? (d) What is the adius of the ion s obit while it is in the egion of magnetic field? (e) Fom the diection in which the paticle is deflected, do ou infe that the magnetic field points into the page o out of the page?

8 Cicle instucto: Moow o Yethiaj 8 Name: SECTION 3: Do TWO () of the thee questions. Each question is woth 4 maks fo a total of 8 maks. Indicate cleal the one question that ou do not want maked b dawing a line though it (don t ease!). [4]. segment (ac) of a non-conducting chaged ing, cented on the oigin, subtends the angle fom 6 to 6 as shown. The adius of the ing is.45 m and the linea chage densit on the ing is 7. C/m. (a) Without doing an integal, what is the -component, E, of the total electic field at the oigin due to the entie chaged ing segment (fom 6 to 6 )? (b) What is the contibution, de, to the component of the electic field at the oigin due to the chage dq in a segment ds at angle? (Hint: think about how to wite dq in tems of the adius of the segment and the angle, d subtended b the segment ds.) (c) What is the -component, E, of the total electic field at the oigin due to the entie chaged ing segment (fom 6 to 6 ). (Integals ae povided on page.)

9 Cicle instucto: Moow o Yethiaj 9 Name: [4]. Two sliding metal bas of length l = 5. cm ae moving along two paallel ails, in opposite diections, with constant speeds of v =.6 m/s, as shown in the figue below. The ails ae located in a unifom magnetic field with a magnitude.47 T that is diected into the page as shown. (a) Calculate the ate of change of the magnetic flu within the loop fomed b the slides and the ails. (b) The total esistance in the cicuit is 5. Ω. What is the magnitude of the cuent flowing aound the cicuit? (c) In what diection does the cuent flow? Indicate this cleal on the diagam and biefl justif ou answe. (d) What foce (magnitude and diection) must be applied to the ight slide to keep it moving at constant speed?

10 Cicle instucto: Moow o Yethiaj Name: [4]. Two infinitel long wies un paallel to the -ais (which comes out of the page in the pictue). Wie # caies a.5 cuent into the page at.3 m, m and wie # caies a.5 cuent out of the page at.3 m, m as shown..3 m # O.5 (in).3 m.3 m (a) On the diagam, daw and label the contibutions fom wie # and wie # to the magnetic field at point P which is located at cm,.3 m as shown. (b) Calculate the total magnetic field at point P. Epess ou answe in unit vecto notation. 9 (c) Imagine a paticle of chage q 3. C along the diection though point P 5 with a velocit v 5 m/s kˆ. What is the foce on this paticle? Epess ou answe in unit vecto notation. (d) What is the foce pe unit length eeted on wie # due to the magnetic field fom wie #? Epess ou answe in unit vecto notation. P #.5 (out)

11 Cicle instucto: Moow o Yethiaj Name: Some Potentiall Useful Fomulae: d q q F ke ˆ dt q k E k ˆ e qi E ke ˆ i T i i v f dq E ke k sping ˆ m E E d g L qinside E mgd I V k v T v t e V k e V ke q i qi i dq U U k e qq q E ds U qv V l R I F qv F I l I F I a ds ˆ d I 4 F II l a ds I d d N dt c E ma c ma d sin I I cos c n v n / n d F / m b m sin bight m m,, dv dv dv E iˆ ˆj d d d V V V E ds kˆ Equations of Electomagnetism (Mawell s Equations): q inside d E d E ds d dt ds I Phsical constants: N m / C 4 k e 8.85 C / N m g 9.8 m/s 7 4 T m / 9 e.6 C m e d dt E 9. c m/s kg Mathematical fomulae cos sin iˆ ˆj kˆ ˆj kˆ iˆ kˆ iˆ ˆj iˆ ˆj kˆ Roots of a b c ae: b b 4ac a 4 V 3 3 sphee sphee sin a d a cos a cos a d a sin a 4 d a a d d a 3/ 3/ a ln a a a d tan a a a d d ln

MAGNETIC FIELD INTRODUCTION

MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),