This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 7 f' 6
Your name: 01 l J‘ v i» {Unlike/m; PHYS 1304, Homework assignment 2
Due September 15, 2009 Problem 1 A circular ring made of an insulating material is cut in half. One half is
given a charge q uniformly distributed along its arc. The other half is
given a charge +q also uniformly distributed along its arc. The two
halves are then rejoined with insulation at the junctions J, as shown. Ly If there is no change in the charge distributions, what is the direction
of the net electrostatic force on an electron located at the center of the circle?
1. Toward the top of the page
@ Toward the bottom of the page
3. To the right
4. To the left
5. Into the page Briefly explain your reasoning. {Igfﬁj I w if {lib l: {p p: Way ,yxﬂury '1'; I; M (33541,; if? [115/0 ! ‘1! “44:5! éill/
a c m 9 0:43: #7 of [41:70: 0wsz 9 4.1: h». rtozl ("3% (571,? Q. [WW K
811’." 1"“. p?:,ﬁ{.l‘fl{\: ' (J SOW‘ETM‘V‘ ; 7 Cam Skim/9}“?! Sf/W W‘Q'JJ‘I’y DUST/w: ,awirw FT WQQr/AV‘) {05"th 1 ‘ F s' .
4% all“ a; as?" m; +2», comm/V 9%“ HM mm 1:: 5Lw'M«lpl I”
.1 g 1» y A ‘ . ‘ A, My \ ,_ PM,“ 5'; w}; a lick lGrJ rm p CMV:“€£ Mﬁﬂﬁdy‘h 4' 5' “79 0 inc. VIM/0H,» CW. v o 'i'l’Vﬁ Hopi4"", “TEE/‘0‘ Owl Q (i 9f>chrm5 vii: locrl'i'cm {51"7'2’270 “("767
. r, J ' l w Problem 2 Two uncharged metal balls, X and Y, stand on insulating glass rods. A
third ball, carrying a negative charge, is brought near the ball Y as
shown in the figure. A conducting wire is then run between X and Y
and then removed. Finally the third ball is removed. if i: Air in {it in}; ‘i‘fil‘i'if When all this is finished
© ball x is negative and ball Y is positive.
2. ball X is positive and ball Y is negative.
3. balls X and Y are both positive, but ball X carries more charge than
ball Y.
4. balls X and Y are both negative.
5. balls X and Y are still uncharged.
6. ball X is neutral and ball Y is positive.
7. ball X is neutral and ball Y is negative.
8. ball X is positive and ball Y is neutral.
9. ball X is negative and ball Y is neutral.
10. balls X and Y are both positive, but ball Y carries more charge than ball X. Briefly explain your reasoning. if ! x . , ‘ .
. l‘ . ‘ \ l ,v  ’ a '_
«’50 ,icqni x gr? " 3" “i '. r . "I; law’le Dal ‘ M42 “L ‘\ lapM 6" ‘~ (“ V’Jlig
i X elim V in X, Y Po; iii: / my! if H a mi» N , _ ‘ \ _/_.
:if c u, , v _, > Mr] L . g 3“ Problem 3 Two identical conducting spheres, A and B, carry equal charge. They
are stationary and separated by a distance much larger than their
diameters. A third identical conducting sphere, C, is uncharged.
Sphere C is first touched to A, then to B, and finally removed (to a far away distance). As a result the electrostatic force Ff between A and 13, which was originally Fi, becomes Ff=(1/2)Fi
Ff=(1/4)F. . @Ff=(3/8)Fi
7. Fi
8. Ff=Fi
9. Ff=OFi wewve Explain how. you arrived to your conclusion. I >
The! “(:19 “ET: {*«ﬂaﬂ'iii‘: VF. i * ‘h’kl o QAL/QAA{L{ ("6"! ( C“ "~,~ 7* ,g“; . k ‘1 ’ > ,, I ‘ .
t5 OL‘S‘Kﬂbijb‘k/éff” “a?” “a u . .: “H.ch 3515.62! rM" c r; ! / / ,r s ’7 £ ,‘ x , f I v i ‘
L\ * L, it: H {m f .3 ~; I ,7; ra; f A; :4. ‘ f to _ I u , 9‘3 “5" “fl; “w ("OJ {‘3‘ ‘ A if * ﬁx 1' ‘(M x L»!
N f #1! n ,I i. s», t \ (1. I.“ I! .1
l . « u t x ~ ~.l i ‘ . I .i :24?
.4] *5... r )k i l L g v . I,
C n ’w‘ . a». , If” i w I ~ " ' 'i ' 5; Ct mm 4 a
Problem 4 r ‘ A ’L¥”'\\“‘<) {Mimi (,t'iiaiige‘s of 3 ('3 2m" lut‘ékflfﬂi in the
.1:y~»p§2uu:n one at ll {11. 33:3 111‘} and the oti‘ic’w 311‘.
{Si} m. {,l m). Fémi the Liiaguéiinclo of the <i>i<=u“l‘;fi<' livid at:
tile might (£110 to thaw» two Villli‘fgﬂtri. Alls'\\7<*’l‘
in {Hilts of f0. Finrl the single l")("‘1"W{;"("'I1 HM" \W‘lzcn“ for The
clmttric livid at the origin “mi a \“t‘tf‘fui‘ in tile .T'J minus .1thlifriiction. ..~"\.111;~sw<\r in units of 1. Sketch and clearly label the coordinate system, positions of
charges, point where the electric field is measured, the vector of
the electric field, the vector V in the minus Xdirection and the
angle in the last part of the problem. If it makes sense to assume .__/ that V is a unit vector, do so. 3‘ “a V (I. ’ e r 2. What are the components of the electric field? What is its
magnitude? Answer in terms of equations before plugging in the numbers ' : \ i, '
C?
.‘ r
7:2! 1
l; i‘ {A “’8: . 4' in; L",l~ amn/ u,
3. What are ’the components of the vector in the minus x direction? Given the components of the electric field and vector V, what is
the angle between them? Write down an equation and solve for the angle numerically Problem 5
Given :: sqimi‘t‘ with side a. Citzuigos 21.1? A B _
piavoci Hi" E1511}? («jititot‘s oi" at. Miniuw oi <".§.12u'1;:<:> Q I 
(9:1 —ql (:28 :'.:::::‘. .::'.'.::': “R'hi QB :.::.:: —q. ~, ; i \L
Eros;)vvl'é‘vvév {:st {ignite}. :  ‘ T' h i' '
i rote: "the Enin=*i§1:1:;; is ('inc'riuvistzn " ' ‘ ‘ : I) ( ‘ Determine the direction and magnitude of the electric field 59 at center 0. Determine the magnitude of the electric field EC at C due to the charges AB and D. Determine tang, where 9 as the angle between the horizontal line and the electric field at C due to the three charges at AB and D. 1. Which principle is used to compute the total force of several forces? 1 )M set»! M r =? a r l ,r :‘ 2. Sketch the coordinate system in the figure and start with the electric field
at 0. Write down x and y components of electric fields created at O by A,
B, C, and D. From this, find the x and y components of the total electric
field at 0; then the magnitude of O; sketch the direction of the electric field at O in the figure 3. Repeat the'sameproce/dure/for C: write down x. and y components. of
electric fields created by A, B, and D; find the x and y components of the“ total electric field at C; then the magnitude of C;_then tanfe’. n \/ ~= 
. ,\ l 7: ,‘\ A 7, v v > 5’ c A L V NProblemG Eight Paint. Charges
3331,13. t”;1l<'11111.‘‘~. luuuvriz , 2» 1 lililb
ill?)
3., it” Hf “jg111x 1’}i'vilil 471:12113ggﬁe. mph ml" 111:1;411i—
Hlulu 22 fl Ill—3' (:1. is luwe‘itrid I51] lllv M IJ‘.11I'I“~s Hal «‘1
Mllw with sides: ml leauglir :3 in :15: slim.311 in ill" 11211112 Final tho? 1*—<%u,.>1111‘1u111mm: ml iiw 1‘; drink: gm! T Wu
t’fxrl‘lmpl H11 the“ tx‘he'trga‘= liléi‘ﬁl’i‘i'l nit painlﬁ A luv?"
l'lli" Milli.1" c’lml’m‘ls, AIIIBR‘LFT 111 11111th i if N: 1. Before proceeding to the calculation, enumerate charges in the
figure, with 8 corresponding to the charge at point A. For each of
charges with i=1...7, visualize (or sketch) the vector of the force Figs exerted by this charge on charge 8. Which of these forces have nonzero x components? Flag 3 Flag 9 ﬂag} ﬂag 2. Add all nonzero xcomponents of the electric force analytically
[33 . F gi:%0:l<fz:.; F :K :13— r
lagx 1 tax ‘ ((5 f2 2 ; Hg): W562 5 E: k}: “0+2. 3. Evaluate the resulting x—component numerically P5115»? Jli',!*2z:.:i"1f$ We Hi 7 ir—Qflxios N Problem 7 Hanging {:Tl'lrirgcs
33MB. ralzrlllllr‘». 11111111."!in(7. L22» ‘1. mini,
(I34 Given: 9 : ELIE lllflf‘égi 'UEV‘BCIJ' iélt‘lliiull 8111122111 i”ij£l,]."v_~‘,l“¢i1 ﬁlrhwl'iﬁra 11.31134,
in equilibrium with eqlial masses an“ alumni. in
l 11*» ilgﬂll‘u Til“ lung 11 ("if 131“ Mil l‘iIl‘Uth 31]?” ilii‘llgll
and the single ifaiwmi in {he [immuij with 1114*
W?“ 1! :11 1%.»; iilmrl lull.
ﬁiWiﬁf‘ﬁiﬁﬁﬁﬁﬁ {a
)_ ’4’" ﬁ w; ,0 Q“
{3; (i «p {Z} l mu 1mg!" Find the 11142.1;1111‘11ilw Hf the r‘llairgv iféll mwli
spharei Aim“ ‘11:“ 111 units of," (1‘, 4. Draw a sketch showing the forces exerted on each sphere.
Describe the type of each force in words ;T’ T; {mac Morris's? F“ ;F,‘ ‘
 >> \‘ 761 = gram“;
Iv: we, ~ )3 I ’ ﬂ
+9 8 Fee x eUC‘t’A/(‘C ’{WQ (fermty
*; i6 5. Which physics laws will be needed to solve this problem? What
does "equilibrium" mean as far as the sum of forces on each
sphere is concerned? Write down equations describing equilibrium, separately considering the sum of forces in the vertical and
horizontal directions Néuffoh’ﬁ was] low Coulomb: E
“Equal/Ciph‘um” WXQMS 'H/LQ gum: fry/“(.125 cm ecu/l4 Sfmei‘ﬂ 204/0 :5 :“ T9100 *— Fe 740 1..., “1— Zzi‘y {£55.le : 6. Solve the equilibrium equations for the magnitude of the charge in
an analytical form 2 x Tm i ‘ $lZI=1aS§n9 Ti??? YE: 3. a SIMS 7. What can you say about the sign of the charge?
I . . , .
(Ne (Cw. not {ml (Wrif «the. 338 Y1 of HA2 (MM 99.. “UMLM {'0 M
I, , J J _
My.” waiim PM: 411" cl» omLté we Cam Vhakg 3M6 "3
this lime, We Saw», a3 7 9M} V'WFQL each 8. Find the value of the charge numerically. Does it make sense? Problem 8 A rod 14 (“111 30115;; is uniformly <~11z‘11‘5:;m1 and
has ei i‘nl’ztl charge of —2‘3 ,uCT. Dmit‘l‘lliilw flit". Liietgiiiéiiulv ul’ tin." electric
ﬁeld 211031;: the axis uf the rmi an“. a point :jij cm
from the, {‘(‘iiful‘ of fhtf‘ rm}. AEJH’WVI‘ ill units 0f N/(Lﬂ. 1. Sketch the coordinate system, the rod, and the point where the
electric field is measured. Also show any distances that may be necessary. How many spatial dimensions does the problem
effectively have? ,A _ V ‘ _ _,,_,.,/\m.,W
O ‘ ' > X"
I «3.256% 2. According to the problem, charge is distributed continuously
on the rod. Write down an equation to compute the electric field
E(r) for a continuous charge distribution. Simplify this equation
by writing it only for the relevant coordinate component(s).
How do we compute dq in this equation? 3” .. “A,Qi ‘
7/152, {gig/iém/ grow"? 6/ i m 1'3 ’1
j, J ~~ A f v
tiri}: Iii 1141;?) r r whérﬁ {)(Tl‘) i€ pila’7c
L... {17.5 A, JimchICIEM§ ,i xvii“; 222' , «we: we . {20
[/‘il’lear‘ O/Léifyif Wit”??? / . AdX 3. Evaluate the resulting integral(s) for E(r) analytically. Write the
final equations, and evaluate them using the explicit numerical
values given in the problem. 9‘ i ‘L‘fLL a K
“s W10 g in rrrrr ‘9’ fix£0.23?) ...
View
Full Document
 Fall '08
 Ye
 Charge, Magnetism, Electric charge

Click to edit the document details