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Unformatted text preview: PHYS 2212, Test 3, November 5, 2008 Name (print) ____________ "liganuL __________ _; ___________________________________________________ __ Instructions Read all problems carefully before attempting to solve them. Your work must be legible, and the organization must be clear. You must show all work, including correct vector notation. Correct answers without adequate explanation will be counted wrong. Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything
you don’t want us to read! Make explanations correct but brief. You do not need to write a lot of prose. Include diagrams! —3 6
Show what goes into a calculation, not just the ﬁnal number, e.g.: :43 = W =
5 X 104 Give standard SI units with your results. Unless speciﬁcally asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula
you need is not given, you must derive it. i If you cannot do some portion of a problem, invent a symbol for the quantity you can’t
calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge “In accordance with the Georgia Tech Honor Code, I have neither given
nor received unauthorized aid on this test.” Sign your name on the line above PHYS 2212
Do not write on this page! Problem 1 (25 Points) A circuit is constructed from two identical 1.5 V batteries and two wires, as shown. The wires are made
of the same material (tungsten), and have the same length (50 cm), but have different diameters: the lefthand wire has radius 1.0 cm and the right—hand wire has radius 0.5 cm. The electron mobility of
tungsten is 1.8e—3 (m/s)/(V/m). Tungsten has 6e+28 mobile electrons per cubic meter. V B Battery #1 ‘G Bit #2 ,l l " Ill .
36'ny BGFEDCB Osiva’fctwf’ E D E1 3+AV,+AVZ :0 j v e m
* " ' A  :: , £2)
E 1,9Ll E1 (19.1: A) 5: Ra.” QR\ ’> AV; “Al/i '
(a 5pts) Complete the graph for the potential vs. position along the circuit. :. AV, "‘ a Avg algay
'.===. _. (b 6pts) On the circuit diagram, draw the electric ﬁeld vectors at each of the 6 points indicated by X. Pa attention to the relative size f our vectors. . . '— __ "
y i:\ MAO yy{ .3 T 18 Same. 35 E1 ' 1" Eu
(c 7pts) Calculate the agnitude of the electric ﬁeld at point C. Show all your work, and express your answer in N/C. (AV; .. AVL: "“ EI'AL’). 1% :. ~Ez.(0.5> CY :. M a I (d 7pts) How long does it take a given electron to travel from one end to the other of the thin wire?
Show your work, and express your answer in seconds. Veloc‘da a} 7' Ué Qzélr; '35}; £1:
at v etc“
3 Problem 2 (25 Points) . (a lOpts) A particular capacitor has a separation between its plates of 0.03 mm. The area of one plate is
16 mg. The capacitor is initially uncharged. Draw a graph of the amount of charge on one plate of the
capacitor vs. time, starting from the moment the capacitor is connected to a bulb and two ordinary 1.5 V
batteries. Your graph should extend slightly past the time when the bulb goes out. charge (b 15pts) The circuit remains connected several minutes after the bulb has gone out. How much charge is
now on the positive plate of the capacitor? Start from physics principles. Show your work clearly and
express your ﬁnal answer in Coulombs. C:
3Q2CV:6‘ _ .
/I——————————.— Problem 3 (25 Points) . At a particular instant a proton is moving with velocity (5.5 X 107, 0,0) m/s, and an electron is moving
with velocity (5 x 107, —5 X 107, 0) m/s. The electron is located 1.5 x 10—6 m below the proton (in the y
direction). ' 5::
N
a
‘9
0..
“1
\4 o , “r 5 (our ofpage (a 4pts) On the diagram draw an arrow representing the electric ﬁeld at the location of the electron, due
to the proton. Label it Ep. (b 4pts) On the diagram draw an arrow representing the magnetic ﬁeld at the location of the electron, due
to the proton. Label it Bp. (c 4pts) On the diagram draw an arrow representing the electric force on the electron at this instant. Label . it F51 . (d 4pts) On the diagram draw an arrow representing the magnetic force on the electron at this instant.
Label it Fmag. (e 9pts) Calculate the magnetic force on the electron at this instant. Your answer should be a vector.
Show all work. T: : Worm) Te: ~i.em“"‘c
:; <5x\b7,—SMD7J '5). m/J V;
‘ fW‘ i: <2: 4i WED Problem 4 (25 Points) An electron moving with a velocity <2 X 107, O, 0) m/s enters a region between two parallel plates that are
6 mm apart and have a potential difference of 200 V. The electron is deﬂected toward the top plate. Eluﬁ'muo
Fm. avatar «an!
A g r is at». *C'k + Pm“
y g g P‘DOe's»®Pl’W
x
Z (a 5pts) At the location of the electron, draw the the electric ﬁeld vector due to the parallel plates and
label it E. (b 5pts) At the location of the electron, draw the electric force vector acting on the electron and label it
Felec (c 5pts) At the location of the electron, draw the direction of the magnetic ﬁeld that has to be applied if
the electron is to travel between the plates without any deﬂection, and label it B. (d 10pts) What is the magnitude of the magnetic field for which the electron travels between the plates without any deflection? NO 6F e.“ é m mag ‘ C.
PM: ' QWC— 95%. AL ’
5.22%" m :. 229‘s
CND ’q
of \ex : \Exm“T ; team T I /\
b'wed‘lm ‘5 $1 "HZ‘ . This page is for extra work, if needed. Things you must know Relationship between electric ﬁeld and electric force Conservation of charge Electric ﬁeld of a point charge The Superposition Principle
Relationship between magnetic ﬁeld and magnetic force
Magnetic ﬁeld of a moving point charge Other Fundamental Concepts _, d1? d" ~ d_' _. .
02E 31%: net ﬁandd—fzmaifv<<c
AUez = qAV AV = —fiondl z —Z(E$Ax+EyAy+EzAz)
@elszlﬁdA @mangggﬁd/l '
fﬁoﬁdAzw fﬁoﬁdAz
E0
 a do  
lemfl : fENC . : drgag . : .U'O ZL‘nside path
_. _. (I) —» d v A
emf I: fENC O = d dimly f B . = M0 [inside path + 60% . ndA
Speciﬁc Results
—» 1 2 s . —» 1 qs .
’Edipole,a$is ” 47(60 Ti?) (0n ax1s, 7“ >> 8) lEdlpole z 47TH) E (on J. ams, 7° >> 3)
c 1 Q . .  a
E = —— J. f t l t d l t 2 , = E 
rod 4WD T T2 + (L/2)2 (7‘ rom cen er) e ec I‘lC IpO e momen p qs p (1 applied
—‘ 1
Emd = ——Q———— (r J. from center)
47T60 “H”? + (L/2)2
~ 1 2Q/L . ~ 1 qz .
z . 2 __ 1
Brad 471.60 T (If 7" << ‘Emng 47760 (Z2 + R2)3/2 (Z a 011g 8X18)
~ Q/A z . {a Q/A[ z] Q/A ,
' = — ——  z — — x f R
‘Edzsk 260 1 (Z2 + R2)1/2 (2 along ems) Edzsk 260 R 260 (1 2 << )
 A a A . . .
Ecapacitor Q Q/ (+Q and ——Q disks) Efmnge x Q/ Just out51de capac1tor
60 60 AB = ﬂIAl X T (short Wire) A}? = IATX E
471’ T2
~‘ ﬁll/0 ~,LL02I a. _1—o l
I wzre — ~ (7’ < L) ‘Bwn‘e — Bearth tan6‘
a _ M0 217TR2 ~ M0 21'7rR2 , _ _ 2
{Bloop —EW~E 23 (on ax15,z>>R) M—IA—IWR
~ 2 . ~ #0 u .
leipoleyaxis “ fit—7:7? (011 3X13: 7” >> 8) ‘Bdipoleyi’ ~ 55 (on J. ax1s, 7" >> 5)
 E d
' _ 1 —qaL A _ A A  _ m
rad — 471,60 C2T 1} — rad X Brad Brad — C
1=nA77 I=qnA17 UzuE
I L
0=qnu Jzing R_a ‘ * Eu '6 1 1
t Edielectric = ppm d AV = q — — — due to a point charge
K 47TEO Tf T‘i
. IAVI . . .
I = R for an ohmlc res1stor (R Independent of AV); power 2 I AV
Q = C AV
AV . .
Q = C IAVI Power = I AV I = (ohmic res1stor)
. d' ~ 2
K % émv2 1f 1} << 0 circular motion: E—i = % z 17%
Math Help
{ix 5: (awawz) >< (bz,by,bz)
= (ay bz — a; by)§: — (ax bz # a2 1275)?) + (aan by —' (1y bw)2
/ dav 1 ( + ) + / d3: 1 + / dm 1 + C
: n ——.._— 2 _ C —_ = A.__.___
ac+a a m c (a:+a)2 a+ac (a+x)3 2(a+ar)2
‘1 2 2 a 3
/adav=ax+c /a$dm=§x +c /a$ daz=§x +c
Constant Symbol Approximate Value
Speed of light c 3 X 108 m/s
Gravitational constant G 6.7 x 10'11 N  m2/kg2
Approx. grav ﬁeld near Earths surface 9 9.8 N/ kg
Electron mass mi3 9 x 10’31 kg
Proton mass mp 1.7 X 10’27 kg
Neutron mass mm 1.7 x 10‘27 kg
1
Electric constant 4 9 X 109 N  m2/C2
7760
Epsilonzero 60 8.85 X 10—12 (N  m2/C2)_1
Magnetic constant 5—0 1 X 10—7 T  m/A
7r
Mu—zero no 471' x 10—7 T  m/A
Proton charge 6 1.6 X 10’19 C
Electron volt 1 eV 1.6 X 10‘19 J
Avogadro’s number N A 6.02 X 1023 molecules/ mole
Atomic radius R, x 1 X 10‘10 m
Proton radius Rp % 1 x 10—15 m
E to ionize air Eicmize z 3 x 106 V/m
BEarth (horizontal component) B Earth % 2 X 10‘5 T ...
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This note was uploaded on 04/10/2011 for the course PHYS 2212 taught by Professor Kindermann during the Spring '09 term at Georgia Institute of Technology.
 Spring '09
 Kindermann

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