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Name & Section Saunders Physics 133  Electromagnetism Exam 1 ° You must do and show/explain your own work. Partial credit will be awarded. However,
a correct answer without explanatory material will not receive full credit. 0 Clearly indicate your ﬁnal result with a box or circle. 0 If you need more space go onto the back and indicate "OVER". Possibly helpful information: NOTE: These formulae just give the magnitudes. You need to
determine the direction. F =qE point: E Kq , F — Kq‘qz =_2 point points  r2
  . _ Q . . _ g
lmear charge dens1ty. A  I surface charge den31ty. n — A
“inﬁnite” line: Eline = gK—A “inﬁnite” plane: Eplane = '—n—
r 280
ideal capacitor: E = ﬂ—
£0
4): = :EAcos(0) Gauss’s Law: 4): = Q‘"
80
surface area of a sphere: 4J'L’r2 , K = 1
4Jt80
£0 = 8.85x10'12C2/(Nm2) e=1.6x 10‘9c, K=9x109Nm2/C2 V Page 1 of’7
kaS 4/17/05 133505x1.doc Q1. (20 pts) Point charges are at three corners of a square of _ 1
side a. q1=  q, q2= +4q, q3=  q. A 1g pith ball with charge
q4=lnC is placed at point P at the other comer. 1 (a) (Spts) On the diagram indicate, using arrows, the
direction and relative magnitude of the force acting on the
pith ball at point P due to each charge. (You should show 3 vectors at P.) t\§° 3
“ ” "‘9
LI 1 .. 1 (b) (10pts) Determine the net force (in component form, i.e. i and j) experienced by the pith ball,
if q=1nC and a=5cm. ‘7.
t we”
F : Milli.“ _ (Elam) .: 3.5VID"" Ng‘ /
r m 9 “rahz ‘ o.os ~ 6,»? 3 : (“’“lP‘W’Dqll‘ww : mwﬂ K mm“ (0‘ 0§ 52.31
. '._ l
f; w % 2 mm a: my mm mm _ ..t / — 2
{Wm  _ év 10 N I)
a ' (o .6331
4 g. ‘7 ‘\
a =   .w )t +
{emf : “7.2xronws “6°? — 725Jn45 3‘ FM? (1pm 5 ‘0 *95‘0'3wopys
_ m g 3M Io  ’
e‘io‘lxr («Snow/Io J .3 A. 6 a
45m : ammo N2 + goamo‘ M?
(c) (Spts) Determine the magnitude and direction of the initial acceleration experienced by the K pith ball. You can specify the direction by drawing a diagram and calculating the appropriate
angle (as I did in class). m Mu.
» maﬁer
b a.» xwwm'l Wm» munwu
m; ‘ , 1X GM ‘9 (empowd‘g A/«L, g A m a
' ’— 4 P ql 59 ”
.(S‘Oqsxmday‘a (3,OQIWO“>~Z I (o. (DO/£55“ /
L4" 3 7WD“6 A! 3. (mom 9%,) a kfcs 4/17/05 133505xl.doc Page 2 of 7 /T\
y
Q2. (20 pts) A thin rod (length L) with total charge Q (>0) is situated E
between y=a and y=b on the +yaxis. We are interested in the electric b I
ﬁeld on the x—axis at some point P=(xo,0). m"
(a) (8 pts) Write an expression for the x and y components of the
electric ﬁeld at P due to a generic chunk of charge dq located at a , Ag ‘ at position (0,y) on the rod? $0M V
f :W" g, f
a? ' A
x .____.._._._
E : ’4
A
,_r (b) (12 pts) Now write an expression for the total electric ﬁeld at P. These should be 2 integrals
involving ﬁe variable and constants in a form that could be looked up. Do not evaluate the integrals. is an ’3: Variables, _memmmmn u s
W“ M b
kfcs 4/17/05 133505xl.doc a
K Page 3 of 7 Q3. (20 pts) We have a "large" sheet of plastic with a
surface charge density n: +2710 on it. Nearby there is
a “long” line charge with constant charge density 4.0. (a) (5 pts) On the “Side View” diagram indicate the
approximate direction of the net electric ﬁeld at “X”. ’1 mama “(3 25 gamma A «HA L Wang 4:; (ﬁance? bi N50434:“ 3d view Side View (b) (10 pts) What are the components of the electric ﬁeld at “X”? (in terms of m, M, b, and
constants) F‘ 3' ’Ef/IO‘M I“ (".2337 ” ” (watt) ‘ "2643‘
Elm Ea ’U‘l‘wz 7: Ex
.. Y no / i 'éo ‘ (c) (5 pts) A point charge (~q) is placed at “X” at rest. What is the force experienced by the point
charge? kfcs 4/17/05 133505x1.doc Page 4 of 7 Q4. (20 pts) A 0. lg pith ball hangs by a thread in the center
of an ideal parallelplate capacitor. The capacitor plates are +
5.00m by 5.00m and are spaced 1cm apart. When the ball has +
charge q = +10nC and the capacitor plates have charge :Q, + r q
the ball hangs at a 30 angle. +Q + .
+
+
+
+
+
+
<—>
lcm
(a) (15 pts) What is the strength of the electric ﬁeld in the capacitor?
‘5
v n”) :fo.°ooIE5‘)(ﬁ.Df§_} E r 3 [lr?*)0‘\'/\/ ng‘N
g” f L! )1 )O '
M£;Wm «w /
é?) =0 T(*‘9.‘BWD“’N>+ 7.94870 1' agar/a '1 C
2.3%“ N ‘ 75.; a 76‘7"
a RV mwmw
Tramsm A! mu, WC /
Q 15,: «:5; = wmwv “has 8’794 1‘ paw”...
r; s: w ~ )o’“5'A/ /
(b) (Spts) What is the charge Q?
_ a; A G _ MS?“
ﬂ ’ T ‘ loos)? p.002é
n N / G? I. 3
F : Q 50 5"”! :00025m1>($’8§4/0./2 /
O
. P, .i r 1
a : @MY’ 0002551 new >
Shiv”?
Q r / l3 7* w” "’ C log ,  5 }%ﬂ
kaS 4/17/05 133505xl.doc ' Page 5 of7 Q5. (20 pts) A point charge ( 4Q) is at the center of a hollow,
conducting, thick spherical shell (inner radius a, outer radius b) that \I/ has its own net charge (+2Q).
I
(a) (15 pts) Using Gauss’s Law determine the electric ﬁeld ' K
everywhere, r<a, a<r<b, b<r, put your answers in the table. Be ‘ecp
sure to give magnitude/direction: e. g.“ 1 %, outward” or similar.
8ﬂ80 r
FOIL Ail. CALCLM A"?! 0N5 : '
a» ~ 941' » F E 5 9L
( « é” " .JA so éo <1
(La 04 : ,qa Egon: "uG‘QQ
f”: M M 2' ~ 2 Q
Am :2.. arr—o Wm M
‘ CE 5: riﬂe I 4‘ (A :0 9869 i. LEM
N417?“ ea 0 ekd'V'4~ '6‘ ‘ ’1’" w awn/:66
/ "SIM a (ancha‘r 'z‘m’ é"
/ ‘/ (b) (5 pts) What is the charge on the outer surface of the spherical shell? Explain your
reasoning. (1:)? ANN (S a clan): a? “VG pm 444.9“, Pavel (Mam.32.) 4M
was/[£3 Sufﬁﬁnum (i Jive gl‘eﬂ HAL/[5+ have a thaw», 016 +qQ
56 5" "l is ”‘ 54H" W“””’""‘""“ Wag/acme, +24. awlv Surthu {VT‘Ol’wyl lam/e ‘1 CL awayk a“? 0% AM SM” m5 4+ ‘4‘. ,—
kfcs4/17/05133505x1.doc 2‘52 (W3 “m "' 2Q) SEE WCﬂ/ggtnm “2G 41: ﬁrearm a. ml chargx ’ l ...
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 Spring '04
 Saunders
 Magnetism

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