quiz1-solutions

# quiz1-solutions - ECE 220 — Quiz 1 Please write your name...

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Unformatted text preview: ECE 220 — Quiz 1 (02/02/04) Please write your name at the top right corner before you start the exam Remember to write the units of. the various quantities that you calculate Use the back side of each page if you need extra space. All formulas and units that you need are given on the last page 1) Give short deﬁnitions or descriptions of the following a) the divergence of a vector D (5 points) The divergence, 09 0c vect—ov D ls'a Scalav eaVL/tal h: the, art/100m? 0C ﬂux 0? Hoe Vt;ch D leaving a closeol serotce'Jott‘x/ioleol b5 .Hia volume (incl/036d. 0175 = 051;; Av. [EV—90‘ b) the Electric ﬁeld intensity E (5 points) it is the, porce exerted on 0L (AME posii'ive Chara}: (1 a) r") F 7:. u/ we 3 5V. c) Gauss’s law (5 points) The, baked eled’vic Chum through a chased SUWCQCE ‘13 eg/mod h: We, aharaa ENC/Lesa} ha Wad: Surpaca. @ if. a? : ca. of J...» <7.sz d) Curl of a vector quantity H (5‘ points) ~> Each wmponen} c3? fine, Cur} M gout/7d b5 EOLKir’Lg {HF/1g (Me inkeargq QC HOE] \f6ch avound a dosed loop Md dividing (Dd W16, qvea anatosed b3 Hne loop weﬂng compone/VP is ‘m a. Oeivech‘on WOTMQI ('2) We (00p. a ,. d; —)> (V X 1(1)) “J = 5%; H \$2: "' AA AA-‘FO. 2) We need to move a charge q (4 x 10'3 C) from a point A, at a voltage 20 V, to a point B, in the presence of an Electric field E, of 1000 _V/m. The direction of the ﬁeld is from point B to point A i.e. we are moving in a direction opposing E. a) If the distance between the two points is 30cm, what is the total work done in moving the charge from A to B? (10 points) b) What is the voltage at the point B? (5 points) — 3 0V : 1;. X l O C - E 2 (OOO V/m. The Force, 50 W16 2., WE : 4 N charaeai) , WOVK done y e oL‘QCexrcmce ’ Vol 0—3 (WE) charge, : .‘ 2;><'lor3 ' 300 V A 3) In electrostatics, the line integral of the Electric field E around a closed loop is always zero. In this case, the relationship between the Electric ﬁeld and the voltage is given by E = - grad (V). Calculate E if a) V = 10 (V) (equal potential everywhere) (5 points) b) V = 5x + 7y (V) (5 points) If we have two points A and B and the Electric ﬁeld between the points is zero, then VA = VB . True or False? Give your reasoning (5 points) E ; —~ greed .1 -— V V _. A A A . ,-avx-§l «avz 5x Ba 92 @) v;5x+75 W) E p572 +7 (Wm) Irma, aIC “(Rivals no aha.ch geldItl/neg Hoaxes no gofce on a chargf a] a ‘ & WOYH dﬂnﬂ M 10/10va 0L 3 iihgeen 4 ﬂ 8 43 zero(lggﬁo> .6 \ l, -% (bnvcrseh4)19 V ,45 C1N1\$F0u®€ (Pay 08 L2 than 3 O ' List of units 1) Charge — Coulombs (C) 2) Work — Joules (J) 3) Electric Field Intensity (E) — Newtons/Coulomb (N/C) or Volts/meter (V/m) 4) Voltage — Volts(V) List of formulas and quantities 1) Gradient of a scalar A (in Cartesian coordinates) ...
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