151 final solutions
DESCRIPTION
physic1TRANSCRIPT
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!" 2557-58
SCPY151 1 1
!" 9 $" 2557 ( 9.00-12.00 .
() 1. ,- . 12 ,- / 0 7 "01 84 "01
2. 4-15!$650( 5 7,-
3. 9 7:4-4-("; !"5(,
4. 9 7:4-,- - !
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1) .D.(?0, !A@6(7 0 (55!E 54-A@?E.740 E (
?049! bc (F191("- (adiabatic) 4-"B () .A@40 E (6) 10 (,)
7BHE Tb 10 Tc ((")
.75 a 5 34 10 1 10 0.12
8.31 400a a
a
p Vn
RT
= = =
6 " ()
5 2000 Kbb a aa
VT T TV
= = =
10 ( ) ( )2/31 1/335/ (0.36)c b b c b bT T V V T T
= = =
( )1/31/3 0.0170.343(0.343 0.017) 0.7 1b bT T= + = + ( )0.01713 0.3430.7 1 1423 KbT + = " (,)
2) .,- (1)
) 4-"BB"- 5E5;49! ab bc cd 10 da
,) 4-"B0$HI (; D."- (F, !("; !"-
520.12 8.31 1600 4 kJab p abQ nc T = =
0bcQ adiabatic = 320.12 8.31 ( 577) 860 Jcd V cdQ nc T = = =
ln( / ) 0.12 8.31 400 ln 5 640 Jda a a dQ nRT V V = = =
4000 860 640100 1004000
ab cd da
ab
Q Q Qe Q
+ + = =
2500 100 62.5%
4000= =
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3) . J0.7E(5-(9 -!5-0 2a @!!0 xy .75 -! ! 4-"BK
(,510!) B .75 P 1 z @! E99!(F00 z ..75 -! ! 54- J0.7"19
0.79 9""!(9 ((," 4E, ! a z 10 )
E
.E I9
0
0
2 2 2 2 1/2 2 2 3/2
22
2 32 2 2 2 2 2 3/2
2 3
0 2 2 1/2
0
cos ( ) ( )tan tan sec
cos
(1 tan ) ( )cos cos
cos sin , sin ( )
sin sin
z
z
z
k dy z dydE dE k zz y z y z y
zdy z dy zd z d
z zy z z z y
k k adE d dz z z a
k kE dz z
= = =+ + +
= = = =
+ = + = + =
= = =+
= =
( )0 2 2 1/22
sin( ) ( )k az z a
=
+
2 2 1/2 2 2 1/2 2 22 2
cos ( ) ( )zk a z k aE Ez z a z a z a
= = =
+ + +
!5-
2 284p z each side
k aE Ez a
= = +
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4) 4-"BK.75 A 19! (0,0,0) cmAr = 10.75 B 19! (10,10,0) cmBr =
10"B
"9!K VAB=VA-VB .790.70.5!9
1 2.5 Cq = E919! 1 ( 20, 10,30) cmr =
2 3.0 Cq = E919! 2 (0, 20,10) cmr =
3 5.0 Cq = E919! 3 (20,5,10) cmr =
( )1/22 2 21 20 10 30 10 14 37.4Ar = + + = = cm ( )1/22 2
2 0 20 10 10 5 22.4Ar = + + = = cm
( )1/22 2 23 20 5 10 10 5.25 23Ar = + + = = cm
9 6 9 6 9 69 10 2.5 10 9 10 3 10 9 10 5 100.374 0.224 0.23A
V
= +
( ) 360 121 196 10 15 kV= + =
( ) ( )1/2 1/22 2 2 2 2 21 230 20 30 10 23 48 cm, 10 10 10 10 3 33.3 cmB Br r= + + = = = + + = =
( )1/22 2 23 10 5 10 10 2.25 15 cmBr = + + = =
9 6 9 6 9 69 10 2.5 10 9 10 3 10 9 10 5 100.48 0.333 0.15B
V
= +
( ) 347 82 300 10 171 kV= + =
( )15 171 kV 156kVAB A BV V V= = =
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5) 1L9"E9,E!0 19 651L9!0 5-4 R 1L9!0 5-
R+d 101L9!0 ! ! L (9 (; L5- , !1L95-40.7 +Q 10L5-4, !1L9
5- 0.7 JQ 4-"B
) K09!1L9! ! (00 R < r < R+d)
,) "9!K09!1L9! !
") ".70.7, ! 7B5(; -(F(M0.7
((7 4-(," 4E, ! Q R d 10 L)
4-N, !(A L5(FE!0 r, R
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6) .!.K01!5!E 4-"B01KL9 VL = 6 k (15!!)
1 1 2 1 2
2 2 1 1 2
2 2
1 1
2 1
12 3k 6 ( ) 9 6 ( )24 9 6 ( ) 6 15 ( )
962( ) 3( ) : 96 33 2.9 ( )3319.5( ) ( ) :12 9 17.5 2.17 ( )
9( )6 4.38 V "downward"L
I k I I kI kI akI k I I kI kI b
a b kI I mA mA c
c a kI I mA mA d
V I I k
= + =
= + = +
+ = = =
= = =
= =
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7) 4-"B19(M (,510!) B .75 P 1 z .501 I 0 xy 5!E
. Biot-Savard 19(M E941 z ,55!
0 02 2 1 1( ) ( )4 6 3 2 6 3P
I IB B a B ba b a b
= + = + = +
8) ) 4-"B19(MH46@( 5,55. 1500 " 10 (@( 10
01K 2.0 1 1
7
300
4 10 1500 2 3.77 10 tesla0.1
NIB nIL
= = = =
,) 5-. , !,55100KL9(9 4-"B, !$ 5-!19(M
,5(96@( 54,- ()
0 0 0.1 0.016 1.6 cm2 2 2
NI NI LB RR L
= = = = = =
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9) ,55!. 100 R=50 cm 7 1 y 5L919(M"!,5 2.0 T 4
11 z 5- (M(!7"! 100 = rad/s 4(,MP 4-"B,5E!75, !1!54-
5,55@!.04-,5575- 9!9 (; !
( ) 2max 100 (0.25)(2) 157 N-mN A B NAB N R B = = = = =
10) 4-"B"9(( ! (self-inductance) , !6@( 5,55. 2000 7.5 (@(
10I;5,!,55(9 2 !(@M(
2 7 2 4
30 4 10 2000 2 10 13.4 10 H 13.4mH0.075
N ALL
= = = =
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11) .!.5!E 4-"B01K i 4!. 1079!( 09!01K i 101!("; K
.19!(5 ( ) 3 Vj tt e =E 65 410 rad/s = 1 20 , 12R r= =
4 61 1 40
10 0.8 10Cz
C = = =
4 310 1.5 10 47Lz L = = =
"-4!. ";
1( ) ( 40)(12 47) 1880 48020 20
12 (47 40) 12 7C L
sum
C L
z z r j j jR Rz z r j j
+ + = + = + = +
+ + + +
( )( )1.9 0.5 12 71881 480 1.9 0.5 26.3 7.3 136 3812 7 12 7 193 193
j jj j jk k k jj j + +
= = = = ++ +
1 1 038156 38 160 , tan tan 0.24 13.7156
jsumR j e = + = = = =
0 03
, 18.75 mA160
j t ji I e I += = =
12) 4";19(MK10@!(5!41 z I919(M41 y "95!9
( , ) ( , )B z t B z t y= 65 ( )8 6 3( , ) (3 10 T)sin (10 3 10 )B z t z t =
4-"B ) K ( , )E z t (,- ! !,510! 10 ,) !! !(J"19!!, !";19(MK (W/m2)
( )
0
6 3
820 0
70 0
( , ) ( , ) ( , ) ( , )
( , ) ( , ) (9V)sin (10 3 10 )27 10 0.11 mW/m
2 2 4 10rms rms
rms
B z t B z t y E z t E z t x
E BS Sz
E z t cB z t z t
E B E BS
= =
= =
= =
= = = =