101_1_mid_term_sol

# 101_1_mid_term_sol - MthfRM éOLLsTIoMJ EElOl Midterm...

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Unformatted text preview: / MthfRM éOLLsTIoMJ EElOl Midterm; Student Name: Student ID# (OPEN BOOKS AND NOTES} (1) (7 ﬁts) Evaluate f0" faznﬂaf - 2 + a? o y + a2" -2|2) (hp d6 + I: Inﬂow + £15? + a2| + as) dcp d6=? (R,t9,go) and (x,y,z) deﬁne the Spherical and Cartesian coordinate systems, respectively. ‘a’ is just a constant where #0. _} “(9%).4449 :1 'ﬁ'Q‘yr ‘ﬁsﬁ' 0° “IT'er GD 2: \3QI1#JQ+ [We c499e19+jfo24¢c49= + a (\$M9a>¢/£45{05M¢; + 0-56 3M5 no \ 4t», TAJ'jM aha-95 not Emlwkd,wz— IS a Menu—7‘5) at Mot @ 1‘ “6133+ 59) (Aﬁr 3%) (2) {20 ﬁts) Determine the initial direction of the deﬂection of the charged particles [i.e., the force acting on the particles! as they enter the magnetic ﬁelds as shown below. The charged particle is entering the magnetic ﬁeld region from the left (as shown below) with a constant speed. The arrow on the charged particle indicates the initial velocity vector of the particle. Draw your answers on the ﬁgures shown below. Also EXPLAIN your result brieﬂy! ##— - (a) E ' 1:1 ("J “'7 "f (9. eq ®®®® . line, \i‘ 1 ﬂ “‘ ‘3 ®®®® 9 AOL abomina- Lsnu should ®®®® puma. ®®®® - AM PW rm; NIL elm” ﬁrm 4 r “57’. t“: (b) @ B - “q :I; “0 all/Hec‘ém , Cr—ss ‘3“ Elf H : Vﬁcﬂ'kﬂf 5 “"1"; _ (C) (3) {21 pts) A perfectly conducting metallic sphere of radius R is placed in vacuum and is loaded with a total charge of Q. You can aSSume Q is positive. (a) Find the electric ﬁeld (both magnitude and direction) everywhere in space, including within the couduc’tor body. (b) Find the voltage at the center (i.e., the core) of this metallic Sphere. (c) Find the voltage at the surface of this metallic sphere (4) (24 pts) You are given a uniform sphere of charge with a radius 1:: and a volume chargedensity of p. This Spherical charge density is located in vacuum. Calculate the amount of electrostatic energy stored in the following regions: (a) inside the sphere. (b) outside the sphere. (c) What would be the additional ener needed to double the radius of the charged sphere to 25, while still keeping the uniform charge density pthe same. (a) R < [o {Dns‘cio—Ju e we} = 4'1. (gm -+E= i; { 2 15-11-er g - W€:%E€Eld\/ — 3-;— R1(R15M9ciedﬂol¢): V o 00 Q 7. 5- b 111" u eel-er we [wet — m 39,93- WT” as @ Wg=liaE2clV = 33% 1“: 122w Ahead -..—. Loo ...
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101_1_mid_term_sol - MthfRM éOLLsTIoMJ EElOl Midterm...

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