!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"#$%&'()!*%+,)'(-%!
!
!
./01
2!3!4-5!
!
!!6!78"9!
#
$
8)-:78;<=888>? @
A%"&% '
(
!
!
21 • [SSM] B!)(5),C#5!)-(C!D#:!.?!',5%:!#%+!#!5#+(,:!-E!?>8!)A>!*'!(:!#'!'D&!
&F,#'-5G!HD&5&!I#5'DJ:!A#$%&'()!E(&C+!(:!8>08!KG!%-5'D>!LD&!#M(:!-E!'D&!)-(C!(:!'D&!
C(%&!'D#'!N#::&:!'D5-,$D!'D&!)&%'&5!-E!'D&!)-(C!#%+!(:!N&5N&%+(),C#5!'-!'D&!NC#%&!-E!
'D&!)-(C>!4(%+!'D&!A#$%&'()!EC,M!'D5-,$D!'D&!)-(C!HD&%!'D&!#M(:!-E!'D&!)-(C!(:!!
2"3!O&5'()#CG!2#3!D-5(P-%'#C!H('D!'D&!#M(:!N-(%'(%$!%-5'DG!2$3!D-5(P-%'#C!H('D!'D&!#M(:!
N-(%'(%$!&#:'G!#%+!2!3!D-5(P-%'#C!H('D!'D&!#M(:!A#Q(%$!#%!#%$C&!-E!18R!H('D!%-5'D>!
! !
Picture the Problem S&)#,:&! 'D&! )-(C! +&E(%&:! #! NC#%&! H('D! #5&#! %! #%+! B
!
(:!
)-%:'#%'!(%! A#$%(',+&!#%+!+(5&)'(-%!-O&5!'D&! :,5E#)&!#%+!A#Q&:!#%!#%$C&!
!
&& H('D!
'D&! ,%('! %-5A#C! O&)'-5G! H&! )#%! ,:&!
!
(
)-:
A'(%
%
'-! E(%+! 'D&! A#$%&'()! EC,M!
'D5-,$D!'D&!)-(C>
LD&!A#$%&'()!EC,M!'D5-,$D!'D&!
)-(C!(:!$(O&%!<T9!
!
!)!(
)-:)-: .
A)'('(% %% !
U,<:'(','&!E-5!%,A&5()#C!O#C,&:!'-!-<'#(%9!
!
# $
# $
!*!)(
)-:;<0>=1)-:A=8?>8
K=8
L=
K08>8.? .
.
@
A%&
+
+
,
-
.
.
/
01% '!
!
2"3!;D&%!'D&!NC#%&!-E!'D&!)-(C!(:!
D-5(P-%'#CG!
!
!!6!78"9!
!
#
$
878)-:;<0>=1
A%"%
*(
!
!
2#3!;D&%!'D&!NC#%&!-E!'D&!)-(C!(:!
O&5'()#C!H('D!(':!#M(:!N-(%'(%$!
%-5'DG!
!
!!6!8"9!
!
#
$
;<=@8)-:;<0>=1
A
**(
%"% !
2$3!;D&%!'D&!NC#%&!-E!'D&!)-(C!(:!
O&5'()#C!H('D!(':!#M(:!N-(%'(%$!
&#:'G!
!
!!6!78"9!
!
#
$
878)-:;<0>=1
A%"%
*(
!
2!3!;D&%!'D&!NC#%&!-E!'D&!)-(C!(:!
O&5'()#C!H('D!(':!#M(:!A#Q(%$!#%!#%$C&!
-E!18"!H('D!%-5'DG!
!
!!6!18"9!
#
$
;<=.18)-:;<0>=1
A
**(
%"% !
!
22 •! B!A#$%&'()!E(&C+!-E!=>.!L!(:!N&5N&%+(),C#5!'-!'D&!NC#%&!-E!#=@!',5%!
:F,#5&!)-(C!H('D!:(+&:!?>8V)A!C-%$>!2"3!4(%+!'D&!A#$%&'()!EC,M!'D5-,$D!'D&!)-(C>!!
2#3!4(%+!'D&!A#$%&'()!EC,M!'D5-,$D!'D&!)-(C!(E!'D&!A#$%&'()!E(&C+!A#Q&:!#%!#%$C&!-E!
/8R!H('D!'D&!%-5A#C!'-!'D&!NC#%&!-E!'D&!)-(C>!
!
!!!"#$%&'(!)*!!!!
!
)+*,!
!
-!.!/#'!01234"
!
5#!$67!&#'!86729'7!'504
"
#!$('!:#;<6!$:!0269&8;6:!;0!$"86!&#'!
0;11;<86=!=($%#>!/#'!:;187!92(?'!('%(':'6&:!
!
54!&#'!7$:#'7!92(?'!('%(':'6&: >
"
"
!
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
0.0 1.0 2.0 3.0 4.0 5.0 6.0
$!-:.
0123
'50
-1.00
-0.50
0.00
0.50
1.00
flux (Wb)
emf (V)
!
!
-%.!@'0'((86=!&;!&#'!=($%#4!<'!:''!&#$&!&#'!0123!8:!$!5868525!<#'6!$!A!)>,!:!$67!
&#$&!&-)>,!:.!A!,>!
!
-'.!/#'!0123!8:!B'(;!<#'6!$"A!,!$67!$!A!C>,!:>!
"
-,."A!,>C,!D!$67!!
"
-C>,!:."A!!#,>C,!D>!
32 • E!:;1'6;87!&#$&!#$:!$!1'6=&#!'F2$1!&;!)G>,!954!$!($782:!'F2$1!&;!!
,>*,,!954!$67!C,,!&2(6:!8:!86!$!('=8;6!<#'('!$!5$=6'&89!08'17!;0!+,,!H!'38:&:!$67!
5$I':!$6!$6=1'!;0!G,J!<8&#!&#'!$38:!;0!&#'!:;1'6;87>!-!.!K867!&#'!5$=6'&89!0123!
&#(;2=#!&#'!:;1'6;87>!-%.!K867!&#'!5$=68&27'!;0!&#'!$?'($='!'50!86729'7!86!&#'!
:;1'6;87!80!&#'!5$=6'&89!08'17!8:!('729'7!&;!B'(;!86!L>C,!:>!
! !
Picture the Problem!M'!9$6!2:'!8&:!7'0868&8;6!&;!0867!&#'!5$=6'&89!0123!&#(;2=#!
&#'!:;1'6;87!$67!K$($7$NO:!1$<!&;!0867!&#'!'50!86729'7!86!&#'!:;1'6;87!<#'6!&#'!
'3&'(6$1!08'17!8:!('729'7!&;!B'(;!86!L>C!:>!
!
-!.!P3%('::!&#'!5$=6'&89!0123!
&#(;2=#!&#'!:;1'6;87!86!&'(5:!;0!
(4")4!*4"$67!
$
"Q!
!
$%
$
!
9;:
9;:
)
5
+()
()*
&
&
!
R2S:&8&2&'!625'(89$1!?$12':!
$67!'?$12$&'!
!
5Q!
'
(
'
(
'
(
5MSL>T5MSL,>T
G,9;:5,,*,,>,5/,>+,C,, )
5
&&
)&
%!
!
!!!"#$%&'(!)*!!!!
!
)+*,!
Motional EMF
36 •• -!./0/123!4567!(58!359':!:&'$8;4<!$&!*0//!3=:!;6!$!%4$6'!&#$&!;:!
%'(%'68;2>4$(!&5!$!3$76'&;2!?;'48!5?!@//!A0!B#'!9'452;&<!5?!&#'!(58!;:!
%'(%'68;2>4$(!&5!;&:!4'67�!C;68!D!E!&#'!3$76'&;2!?5(2'!56!$6!'4'2&(56!;6!&#'!(58F!
D"E!&#'!'4'2&(5:&$&;2!?;'48!;6!&#'!(58F!$68!D#E!&#'!%5&'6&;$4!8;??'('62'!G'&H''6!&#'!
'68:!5?!&#'!(580!
!
Picture the Problem! I'! 2$6! $%%4<! &#'! 'J>$&;56! ?5(! &#'! ?5(2'! 56! $! 2#$(7'8!
%$(&;24'! 359;67! ;6! $! 3$76'&;2! ?;'48! &5! ?;68! &#'! 3$76'&;2! ?5(2'! $2&;67! 56! $6!
'4'2&(56!;6! &#'!(580!I'!2$6!>:'! BvE
!
!
!
!" !&5! ?;68!$! $68 "$%
"
F!H#'('! "! ;:!&#'!
4'67&#!5?!&#'!(58F!&5!?;68!&#'!%5&'6&;$4!8;??'('62'!G'&H''6!;&:!'68:0!
!
D!E!K'4$&'!&#'!3$76'&;2!?5(2'!56!$6!
'4'2&(56!;6!&#'!(58!&5!&#'!:%''8!5?!&#'!
(58F!&#'!'4'2&(56;2!2#$(7'F!$68!&#'!
3$76'&;2!?;'48!;6!H#;2#!&#'!(58!;:!
359;67L!
!
BvF
!
!
!
!" &!
$68!
#
:;6&'()
"
!
M>G:&;&>&'!6>3'(;2$4!9$4>':!$68!
'9$4>$&'!)L!
!
$
%
$
%
$ %
NO/+0,
:;6P/B/0/@//
3=:*0//"O/O0+/)
)/
OP
&
&
!"
'!
!"F
!
!
D"E!QR%('::!&#'!'4'2&(5:&$&;2!?;'48!
E
!
;6!&#'!(58!;6!&'(3:!5?!&#'!3$76'&;2!
?;'48! B
!
L!
!
BvE
!
!
!
!" $68!
#
:;6'($
"
!H#'('!
#
!!;:!
&#'!$674'!G'&H''6! v
!
!$68! B
!
0!
!
M>G:&;&>&'!6>3'(;2$4!9$4>':!$68!
'9$4>$&'!(L!
$
%
$
%
S=3/0,/S=3/0,//
:;6P/B/0/@//3=:*0//
""
'
"
$
!
!
D#E!K'4$&'!&#'!%5&'6&;$4!8;??'('62'!
G'&H''6!&#'!'68:!5?!&#'!(58!&5!;&:!
4'67&# "$68!&#'!'4'2&(;2!?;'48!$L!
!
"$%
"
!
M>G:&;&>&'!6>3'(;2$4!9$4>':!$68!
'9$4>$&'!%L!
$
%
$
%
S/0O)3/0.//S=3/0,// ""%!
!
37 •• -!./0/123!4567!(58!359':!;6!$!%4$6'!&#$&!;:!%'(%'68;2>4$(!&5!$!
3$76'&;2!?;'48!5?!@//!A0!B#'!9'452;&<!5?!&#'!(58!;:!%'(%'68;2>4$(!&5!;&:!4'67�!!
C;68!&#'!:%''8!5?!&#'!(58!;?!&#'!%5&'6&;$4!8;??'('62'!G'&H''6!&#'!'68:!;:!+0//!S0!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"#$%&'()!*%+,)'(-%!
!
!
./00
1,23'(','&!%,4&5()#6!7#6,&3!#%+!
&7#6,#'&!!8!
!
"
!
"
49:.;<
=>;<<
?:<.;<<!@<< A
#
$
#
%
!
!
53 •••![SSM]! 1B-C!'B#'!'B&!(%+,)'#%)&!-D!#!'-5-(+!-D!5&)'#%$,6#5!)5-33!
3&)'(-%E!#3!3B-C%!(%!F($,5&!.GH>.!(3!$(7&%!2I! "#
&
-#.$6% %J&
!
"
.
'
!CB&5&!#!(3!'B&!
'-'#6!%,42&5!-D!',5%3E!&!(3!'B&!(%3(+&!5#+(,3E!%!(3!'B&!-,'3(+&!5#+(,3E!#%+!$!(3!'B&!
B&($B'!-D!'B&!'-5-(+;!!
!
Picture the Problem K&! )#%! ,3&! =4L&5&M3! 6#C! '-! &NL5&33! 'B&! 4#$%&'()! D(&6+!
(%3(+&! 'B&! 5&)'#%$,6#5! '-5-(+! #%+! 'B&! +&D(%('(-%! -D! 4#$%&'()! D6,N! '-! &NL5&33!
(
4!
'B5-,$B!'B&!'-5-(+;!K&!)#%!'B&%!,3&!'B&! +&D(%('(-%!-D!3&6DH(%+,)'#%)&!-D!#!3-6&%-(+!
'-!&NL5&33!";!
!
O3(%$!'B&!+&D(%('(-%!-D!'B&!3&6DH
(%+,)'#%)&!-D!#!3-6&%-(+E!&NL5&33!
"!(%!'&543!-D!
(
4E!#E!#%+!'8!
!
'
#
"4
(
#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!P:Q!
=LL6I!=4L&5&M3!6#C!'-!#!)6-3&+!L#'B!
-D!5#+(,3!&(R!)(R!%8!
!
?<
?.')*+
&'
##)
*!
"
"
B!
-5E!2&)#,3&!'?!S!#'E!
#')* <
.
&
'
#
+)
#'
*
'
&
.
<
#!
!
TNL5&33!'B&!D6,N!(%!#!3'5(L!-D!B&($B'!
$!#%+!C(+'B! +) 8!
!
*$+)+
#
4
(
!
1,23'(','(%$!D-5!*!I(&6+38! +)
)
#'$
+
'
&
(
.
<
4#!
!
*%'&$5#'&!+
(
4!D5-4!)(S!&!'-!)!S!%!'-!
-2'#(%8!
!
,
-
.
/
0
1
## *&
%
#'$
)
+)
#'$ %
&
6%
..
<<
4
'
&
'
&
(
!
!
1,23'(','&!D-5! 4
(
(%!&U,#'(-%!P:Q!#%+!
3(4L6(DI!'-!-2'#(%8! ,
-
.
/
0
1
#&
%$#
"6%
.
.
<
'
&
!
Magnetic Energy
54 • =!)-(6!'B#'!B#3!#!3&6DH(%+,)'#%)&!-D!.;<<!9!#%+!#!5&3(3'#%)&!-D!:.;<!2!
(3!)-%%&)'&+!'-!#%!(+!.A;<HV!2#''&5I;!P&Q!KB#'!(3!'B&!3'&#+IH3'#'&!),55&%'W!!
!!!"#$%&'(!)*!!!!
!
)+,,!
-!.!/01!234#!'5'(67!89!9&0(':!85!&#'!85:34&0(!1#'5!&#'!9&'$:7;9&$&'!43(('5&!89!
'9&$<=89#':>!
! !
Picture the Problem ?#'!43(('5&!85! $5!"#!48(438&@! $9!$!A354&805! 0A!&82'@!89! 68B'5!
<7!
!
"
#
$
%&& $
$% C
A@!1#'('!&A!D!
&
,E#!$5:!
#
!D!"E#'!?#'!'5'(67!9&0(':!85!&#'!85:34&0(!
35:'(! 9&'$:7;9&$&'! 405:8&8059! 89! 9&0(':! 85! 8&9! 2$65'&84! A8'=:! $5:! 89! 68B'5! <7!
)
A
)
C
2"&( %F!
!
-).!?#'!A85$=!43(('5&!89!&#'!G30&8'5&!0A!
&#'!'2A!0A!&#'!<$&&'(7!$5:!&#'!('989&$54'!
0A!&#'!408=H!
!
I)F,,
!C)F,
J)KF,
,
A%%% #
&
&
!
-!.!?#'!'5'(67!9&0(':!85!&#'!85:34&0(!
89H!
!
"
!
"
LKF,,
I)F,,/)F,, )
)
C
)
A
)
C
2
%
%% "&(
!
!
55 • [SSM]! M5!$!%=$5'!'='4&(02$65'&84!1$B'@!&#'!2$658&3:'9!0A!&#'!
'='4&(84!A8'=:9!$5:!2$65'&84!A8'=:9!$('!('=$&':!<7!*!D!+,@!1#'('! ,,
C
'(
%+!89!
&#'!9%'':!0A!=86#&F!N#01!&#$&!1#'5!*!D!+,!&#'!'='4&(84!$5:!&#'!2$65'&84!'5'(67!
:'598&8'9!$('!'G3$=F!!
! !
Picture the Problem O'!4$5!'P$285'!&#'!($&80!0A!-2!&0!-Q!18&#!*!D!+,!$5:!
,,
C
'(
%+&0!9#01!&#$&!&#'!'='4&(84!$5:!2$65'&84!'5'(67!:'598&8'9!$('!'G3$=F!
!
QP%('99!&#'!($&80!0A!&#'!'5'(67!
:'598&7!85!&#'!2$65'&84!A8'=:!&0!&#'!
'5'(67!:'598&7!85!&#'!'='4&(84!A8'=:H!
!
)
,,
)
)
,
)
C
,
)
Q
2)
*
,
*
,
-
-
('(
'
%% !
!
R'4$39'!*.D!+,H!
!)
,,
))
,,
)
Q
2C
+,+
,
-
-
('('
%% !
!
N3<9&8&3&856!A0(!+)!$5:!982%=8A7856!
78'=:9H! C
,,
,,
Q
2%%
('
(
'
-
-!)!Q2 -- %!
!
56 •• I!),,,;&3(5!90='508:!#$9!$!4(099;9'4&805$=!$('$!'G3$=!&0!KF,!42)!$5:!!
='56&#!'G3$=!&0!S,!42F!?#'!90='508:!4$((8'9!$!43(('5&!0A!KF,!IF!-).!"$=43=$&'!&#'!
2$65'&84!'5'(67!9&0(':!85!&#'!90='508:!39856!(!D! C
)"&)@!1#'('!"!D!
'
,/)0!!F!!
-!.!T8B8:'!703(!$591'(!85!U$(&!-).!<7!&#'!B0=32'!0A!&#'!('6805!8598:'!&#'!90='508:!
&0!A85:!&#'!2$65'&84!'5'(67!%'(!358&!B0=32'!85!&#'!90='508:F!-+.!"#'4V!703(!U$(&!
-!.!('93=&!<7!402%3&856!&#'!2$65'&84!'5'(67!:'598&7!A(02 .!!
'
2
%,)1)
'
,!1#'('!!
,!D!
'
,/&F! !
PHY 106 Spring 2009 - Homework Chapter 28