EECE 380 Midterm, Fall 2001

Profs. R. Chedid FACULTY OF ENGINEERING S. Abou-Chahine & ARCHITECTURE TEST ID 1000 (EE078) Field Theory CLOSED BOOK (i % HRS) Programmable Calculators are not allowed Provide your answers on the computer’s card only Return the computer’s card attached to the question sheet Mark with a pencil your name and your ID-No Use pencil for marking your answers When using eraser, be sure that you have erased well. "i! PENALTY 6 TO 1 !!! Nov.10, 2001 Test ID 1000- 1/6 we fin all problems below take 6=(10°/36n); A potential field is given by V=3x’y-yz. Which of the following is not inue: a. b c d e At point (1,0,-1), both V and E vanish Be ag : ae: . x'y=I is an equipotential line on the xy plane ag PSE = The equipotential surface V=-8 passes through point P(2,-1,4) Eng. & Arce Libr: fy The electric field at P(2,-1,4) is 12a, — 8ay -a, None of the above Suppose a uniform electric field exists in the room in which you are working, such that the line of force are horizontal and at right angles to one wall. As you walk toward the wall from which the lines of force emerge into the room, are you walking toward a. egos Plane Z: eRe Fp Suppos Points of lower potential ? points of higher potential ? Points of the same potential? Insufficient information to determine the direction of higher potential None of the above =10m carries charge 20nC/m?. The electric field intensity at the origin is: -10 az V/m a -187 az V/m ANE -72n az V/m : “4g -3607 az V/m cA ao None of the above RNY ¢ the Z=0 plane is the interface between two regions: Z>0 has €)=Se, and Z<0 has €2=3¢,. If E2 =10 a, +20 a,, find D; and E;. eaogep D, =50 a, +60 a, , E; =, (10 a, +12 a,) D, =50, ax +60 az, Ey = € (10 a, +12 a,) D, =€,(50 a, +60 a,.), E; = 10 a, +12 a,-~ D, =€,(30 a, +60 az), E, = 10 a, +12 a, None of the above Test ID 1000- 2/6 5. Consider in the xy plane the 3 point charges shown below. if Qs, =4.10 ? C and Qs =15.10°" Cand Qc =15.10 C, find the electric force exerted on Qa. Qa. OF mm Q. 2 Se [ A : x 0.4 WaEe OuUmm a (7.25 ae +1.72a,) AC Bb. C725 ae=1-F2 ay) Ac c. (1.72a,-7.25 ay) Dae d c (-7.25 a, +1.72 ay) AAC None of the above 6. Two charges are arranged in the xy plane as follows: wd Qi=10°C at (0,1) and Q;=-10°C at (0,-1) 7 prc a OV be Big Vv: c. (10°/4ne,) / [(1(x-1)) - (IM(x+1))] d (10°/4me,) / [(1x+1)) -— (1K(x-1))] e. None of the above 7. In problem 6, find the electric field intensity E anywhere along the x-axis a [-18/(x"+1)°?] (a, ay) V/m b. OV/m c. [-18/(x’+1)**] (a,) Vim ad. [-18/(x+1)*?] (a) V/m e. None of the above Test ID 1000- 3/6 8. The figure below shows a parallel plate capacitor containing two dielectrics with permittivities ¢,, =1.5 and €2 = 3.5. Each of the dielectrics occupies one-half of the volume as shown. If the plate area is S = 2m? and the dielectric thickness is d = 10° m, Calculate the capacitance of this capacitor. 2 ere ose Ld rae C=13.3nF B C=443 nF Yah C=31.0nF C=93 nF Non of the above Calculate the work done in moving a point charge Q = -20 nC from the origin to point (4, 2, 0) in the field E = (x/2 + 2y) a, + 2x ay. 80 uJ 320 py 400 pJ ast 240 pJ ee Non of the above ae ~ . Calculate the stored energy in a system of four identical point charges Q = 4 nC located at the corners of a square, each side of which is 1m long. 780 nJ 390 nJ $76 nJ 204 nJ Non of the above A uniform infinite line charge with p_=5 ,tC/m lies along the x-axis (y=0, z=0). The electric flux density D at the point (3, 2, 1), m, is: 0.356 (2ay + a,) wC/m? 0.159 (2ay + a,) wC/m? 0.356 (ay + 2a,) wC/m? 0.159 (ay + 2a,) wC/m? Non of the above Test ID 1000- 4/6 12. A spherical capacitor consists of an inner conducting sphere of radius Rj and an outer conductor with a spherical inner wall of radius Ry. The space in between is filled with a dielectric of permittivity e. The capacitance C is : a- 4n6(1/R;~ 1/R,)" b- 4ne (1/Ri + UR.) c- 4ne(1/R; — 1/R,) d- 4ne(1/R; + 1/R,) a e- Non of the above rh Ae ‘ 13. A line charge of uniform density pp= 5 uC/m forms a semicircle of radius b in the upper half of the xy-plane as shown. The electric field at the center of the semicircle is : NO a- - (py/2mQb) ay b- -(p,/4i€,b) ay b c- (py/2me,b) (ax + ay) 3 d- (py/2me,b) (ax - ay) aa a e- Non of the above Lt Soy" fa) z, Test ID 1000- 5/6 a Seung « Yl ie gre weld Qui wl, Fole taol~ eo _ a oo tential pete “5 pues by ~eB eo =" Wha le of the ps ee me wor age Bgl At point (1,0,-1) > RE Vanish ® ee ine i “) \ = 2 > ‘yi anemic potted Haye by [2A — P 44-49 amd at right angles wall Foor whieh the Lint4 f pre emerge ito the bie walking Tow and potential ove Cf pere we He ab ; plare Ze lam Carre ares Gone dc@, hts, alts a = ze / AD can A tar at the rimne YU: a a) ~104, V/m Aa! b/ al GIG a) Vjra - 2s og ty vim : ts 4 a 2, c - Js - 5 fp = 340% a7 | ga 2. ¢ ai 4 24n mo on = i prece ee baler fa B27 wee x ae rns 2 ae hay $= 5¢ : = 12 3ts Omd Zag hay 6,’ 2% L & a . fe -Ss Ie “dGignss | 6 ae od ay +204 ae = 3» find Ded E, > _— — s a) Sz TOA, + 6044 ; f= 6.1 1h Mag) e => > > b Ba Be FS cies Ey = & (19 4 +1244 ) 4 5 6) Ba: te (50 a, +604, ); E, = 10> waa —- i a EWS el) a, (308 +60q E, = J34, 2 a), te ee ¢) “me tf ta above 4% D=¢ E “= ¢ > i = Oo q > »( 30a, + 60%, ) ag 8 Ao Tangenti af a B nome’ cout — E£ os - xy Cr Cty = io Qe. 2 Loy 3 é E 25 = é2 € we aS ; , Bx = Se (de) = 412 D=¢ => ‘ , = f.( 508, 4 47 ) wid & . : Ee he HR, wie oe be ee] he capacitance of a paraliel plate capacitor containing two dielectrics, er, = = 3.5, each comprising one-half the volume, as shown where S$ = rr oD rs d= 10° m. a. Ga 199 BF gy hac LPF b- ** C=443 nF tng ce C=31.0nF a C=93nF a re e- Non of the above e. age nee ae a er Te» pone Q pdb Cope cae = Cy + Gi. Hnmilerly Cp z3B1enF => Cnr Cy Ce = Fe Wr. il) The work done Bs moving a point charge Q = -20 uC from the nee to (4, 2, 0).in the field : £ =(x/2 + 2y) ax + 2x ay is: a 80 wJ b- 320 nr c- ** 400 ut d- 240 py e- Non of the above VY) A spherical capacitor consists of an inner conducting sphere of radius R; and an outer conductor with a spherical inner wall of radius R,. The space in between is filed with a dielectric of permittivity e. The capacitance C is : a- ** dre (1/R;— 1/R,)! b- 4me (IR) + IR)? c- 4ne (1/R - 1/R,) d- 4ne (1/Ri + 1/R,) e- Non of the above a ae > on he en. ol aie € Assume Ulorye itl F + uns plot. CSR BAO p VOALEM Pi a = n Za = cy Ath = i Ag cs - eae Re ua ge = WH Ze! Qo. = eae ° \ 218 ae +fsinede— z i RAS ae tod i pe <a boa a ee | a tig 2 dee aVe-| Eol€ ate Re ae ty RS |g Re! . a { ey Se ty FF oo Les Pana a WS. = Va Warnes nae its) ms ‘ yer ute» Sate Se :. _ _ ‘oS BS a s V ge Sie VD LAY re A line charge of uniform density pr 5 uC/m forms a semicircle of radius b in the upper half xy-plane. The electric field at the center of the semicircle is - a a) a- ** - (pt/2m€9b) ay | 5 b- - (p1/4n€,b) ay Ze Bal c- (pr/27€.b) (ast ay) : : aa Ve d- (pr/2necb) (ay - as) Pee e- Non of the above { ee \ te 7 fEdk Bhs i Ne. = 2 Bree ot Le we, hs ite 2 a Ay = eve ax,