#7-Magnetic Forces & Induced EMF 2181

8/18/2019 #7-Magnetic Forces & Induced EMF 2181

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!"#$% '("(% )$*+%,-*(#.%/",(0%$( 12 34#-*5- "$6 7-(,1$10#

389 :;


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=.* B*+-&1*1- '2%) 2+*N

!

F = id !

L !!

B = iLB sin " force on a current,

!

! =!

µ "!

B = µ B sin # = NiAB sin # torque on a current loop,

E = !d "

dt = !

#"

# t Faraday's law,

L = N !

i definition of inductance,

E = ! L di

dt = ! L

" i

" t &":1/)+$5'"$ ;


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?- @()11 A)4"&0- !"B"4&)+> @3)('2,- C#(("4D

N S

Stiff Wire

Magnet Reversing Switch 1 1/2 VoltCell

Fig. 1

-

5.2. Method and Results

E2" 4"B"4&)+> &3)('2 )& 3)4"$ 5+$"4 (2" 8#&"- F*5 G#D )+&6"'( (2" '*++"'()*+ 8D (54+)+> )(*B"4- E2" G#>+"( )& B"4D 6*3"415: #+$ 3):: G#>+"()H" *:$/&(D:" 3)+$/56 3#('2"&- I""6(2"&" #4()':"& #3#D 14*G (2" G#>+"(&-

J"#B" (2)& &3)('2 K#+$ #:: *(2"4& )+ (2"&" "76"4)G"+(&L )+ (2" M*6"+M 6*&)()*+ 32"+N)+)&2"$-

.- O*()+> (2" $)4"'()*+ *1 (2" G#>+"()' N)":$ #+$ (2" '544"+(P ':*&" (2" &3)('2- Q)$ (2"3)4" G*B" 56 *4 $*3+R

?- O*3 (24*3 (2" &3)('2 )+ (2" *66*&)(" $)4"'()*+ (25& 4"B"4&)+> (2" '544"+( (24*5>2(2" 3)4"- O*(" (2" $)4"'()*+ *1 (2" '544"+( #+$ (2" $)4"'()*+ )+ 32)'2 (2" 3)4"G*B"$-

0- O*3 4"B"4&" (2" $)4"'()*+ *1 (2" G#>+"()' N)":$ #+$ 4"6"#( K.L #+$ K?L-

,- ;76:#)+ D*54 *8&"4B#()*+&-

E2)& )::5&(4#("& (2" MG*(*4M 64)+')6#:- =4*G 2"4" )( )& # &2*4( &("6 (* )+'4"#&)+> (2" "11"'( 8D65(()+> )+ # 1"3 G*4" (54+& *1 3)4" 8"(3""+ (2" 6*:"& *1 (2" G#>+"( #+$ '2#+>)+> (2">"*G"(4D *1 (2" &"(56 (* >"( # '*+()+5*5&:D G*B)+> &">G"+( *1 3)4"- S(2"4 6*&&)8):)()"& #4"&5>>"&("$ 8D

!

F = id !

L !!

B = iLB sin " -

!"# %&'& ()! *+ ,


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6. Part II: Detecting the current in Single Wire In Motion in A MagneticField

6.1. Equipment Required

.- +"( ?- @()11 A)4"&0- T#:B#+*G"("4


.- A)(2 (2" &"(56 )::5&(4#("$ )+ =)>- 0 2*:$ (2" 3)4" )+ (2" )+$)'#("$ 6*&)()*+ 8"(3""+ (2"6*:"& *1 (2" G#>+"(- Q*"& (2" >#:B#+*G"("4 )+$)'#(" #+D '544"+( N:*3R

?- 2 (2" 6*:"& *1 (2" G#>+"( KG*B)+> 563#4$&L #+$ #>#)+ +*(" #+D $"N:"'()*+)+ (2" >#:B#+*G"("4- E4D $*)+> (2)& #( $)11"4"+( &6""$&- ;76:#)+ D*54 *8&"4B#()*+&-

7. Part III: Wire Loop In A Magnetic Field


.- +"( ?- @()11 A)4"&0- T#:B#+*G"("4

N S

Fig. 3galvanometer

!"# %&'& ()! *+ -


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97:7 ;#,"-0 4+0 "( (3* &(4#+$& (* 6#&& 8"(3""+ (2" 6*:"& #& )+ =)>- ,- !"6"#( D*54*8&"4B#()*+& #& #8*B"-

?- E4D # :#4>"4 +5G8"4 *1 (54+&P #& G#+D #& D*5 '#+ 64#'()'#8:D >"(- ;76:#)+ )+ ("4G& *16"4()+"+( 1*4G5:#& #+$ '*+'"6(&-

8. Part IV: The Magnetoelectric Generator


.- J)>2( C5:8?- U#+$ '4#+9"$ T"+"4#(*4


.- E54+ (2" '4#+9 *1 (2" >"+"4#(*4 #( $)11"4"+( &6""$&- A2#( 2#66"+&R?- E2"4" )& +* 8#(("4D )+ (2)& ')4'5)( #+$ (2" #66#4#(5& )& +*( 6:5>>"$ )+(* (2" 3#::-

;7#G)+" (2" '*+&(45'()*+ #+$ (2" G"#+& K)-"-P (2" M'*GG5(#(*4ML 32"4"8D (2"'*+()+5*5&:D G*B)+> '*): G#)+(#)+& '*+(#'( 3)(2 (2" 85:8- KV1 #+ *&')::*&'*6" )&#B#):#8:"P "7#G)+" (2" 6#(("4+ >"+"4#("$ 8D (2" *5(65(-L

N S

Fig. 4galvanometer

Fig. 5

!"# %&'& ()! *+ .


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9. Part V: Five Ways to Change The Magnetic Flux (DC)



.- W*): #+$ X"4G#+"+( +"(

)- X:5+>" (2" 6"4G#+"+( G#>+"(P +*4(2 "+$ N)4&(P )+(* (2" &"'*+$#4D '*): #+$*8&"4B" (2" >#:B#+*G"("4-

))- A)(2$4#3 (2" G#>+"(- A2#( $*"& (2" >#:B#+*G"("4 )+$)'#("R

)))- !"6"#( (2" #8*B" (3* &("6& +*3 3)(2 (2" &*5(2 "+$ "+("4)+> (2" &"'*+$#4D '*):N)4&(-

)B- ;76:#)+ D*54 *8&"4B#()*+&- @9"('2 (2" 4":"B#+( :)+"& *1 G#>+"( N:57 (2#( '5(#'4*&& (2" 3)4"&-

?- W*): #+$ ;:"'(4*G#>+"(

A)(2 (2" &3)('2 ':*&"$P 4#)&" #+$ :*3"4 (2" 64)G#4D K3)(2 #+$ 3)(2*5( (2" )4*+'*4"L )+ (2" &"'*+$#4D '*): #+$ *8&"4B" (2" >#:B#+*G"("4- W*G6#4" 3)(2 . #8*B"-

0- X4)G#4D #+$ @"'*+$#4D W*):Y


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)- A)(2 (2" )4*+ '*4" #+$ (2" 64)G#4D '*): )+ (2" &"'*+$#4D '*): #+$ (2" 42"*&(#( #((2" :*3/"+$ &"(()+>P ':*&" (2" &3)('2 &"+$)+> '544"+( (24*5>2 (2" 64)G#4D-A2#( $*"& (2" >#:B#+*G"("4 $*R

))- Z1("4 (2" &3)('2 2#& 8""+ ':*&"$ 1*4 # 84)"1 6"4)*$ *1 ()G"P 32#( $*"& (2">#:B#+*G"("4 4"#$R

))- O*3 *6"+ (2" &3)('2- A2#( 2#66"+& #( (2" >#:B#+*G"("4 "+$R

)B- @5GG#4)H" D*54 '*+':5&)*+ 14*G (2"&" *8&"4B#()*+&- A2#( M'2#+>"M )+ N:57(#9"& 6:#'" 2"4"R

,- X4)G#4D #+$ @"'*+$#4D W*):Y W2#+>)+> W544"+( )+ X4)G#4D

)- A)(2 (2" )4*+ '*4" #+$ (2" 64)G#4D '*): )+ (2" &"'*+$#4D '*): #+$ (2" &3)('2

2":$ ':*&"$P '2#+>" (2" '544"+( )+ (2" 64)G#4D 8D G*B)+> (2" '*+(#'( *1 (2"42"*&(#( 8#'9 #+$ 1*4(2 *B"4 # &2*4( 4#+>" +"#4 )(& :*3/"+$ &"(()+>- S8&"4B" (2">#:B#+*G"("4 $54)+> (2)& #'()*+-

))- ;76:#)+ #+$ '*G6#4" 3)(2 0 #8*B"-

[- X4)G#4D #+$ @"'*+$#4D W*):Y W2#+>)+> X"4G"#8):)(D *1 W*4"

A)(2 '*+$)()*+& #& #8*B" #+$ (2" &3)('2 2":$ ':*&"$P 4#)&" #+$ :*3"4 (2" )4*+ '*4" )+ (2"64)G#4D #+$ +*(" (2" >#:B#+*G"("4 )+$)'#()*+&- !"6"#( 3)(2 # '*66"4 '*4"- ;76:#)+ 2*3(2)& '2#+>"& (2" N:57 )+ *+" '#&" #+$ +*( (2" *(2"4-

10.Part VI: Flux Changes Due to Alternating Currents (ac): TheTransformer


Open Ring

Aluminum Ring

SecondaryCoil

Switch

PrimaryCoil

Platform

Fig. 7. Schematic Diagram of Transformer

!"# %&'& ()! *+ +


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.- X:#'" (2" #:5G)+5G 4)+> *B"4 (2" 64)G#4D &* (2#( )( 4"&(& *+ (2" 6:#(1*4G- Q"64"&& (2"

&3)('2 #+$ 8" 64"6#4"$ (* '#('2 (2" 4)+> #& )( (#9"& *11- KI""6 (2" 85:8 *1 (2" &"'*+$#4D'*): #+$ *(2"4 14#>):" *8\"'(& *5( *1 (2" 3#D-L

?- !"6"#( 3)(2 (2" *6"+ 4)+>- ;76:#)+ (2" 4"#&*+ 1*4 (2" $)11"4"+( 4"&5:(-

0- U*:$ (2" ':*&"$ #:5G)+5G 4)+> )+ D*54 2#+$& +*( G*4" (2#+ 2#:1 3#D $*3+ (* (2"6:#(1*4G *1 (2" 64)G#4D 1*4 .[/?] &"'*+$& #& (2" &3)('2 )& 2":$ $"64"&&"$ #+$ +*(" #+D&"+()*+P )-"-P 2"#(- ;76:#)+ 32#( )& (#9)+> 6:#'"-

,- A)(2 (2" &3)('2 2":$ $"64"&&"$ 2*:$ (2" &"'*+$#4D '*): *B"4 (2" 64)G#4D #+$ :*3"4 )( (*(2" 6:#(1*4G- ^+:)9" )+ (2" 64"B)*5& "76"4)G"+(& D*5 $* +*( 2#B" (* G#9" #+$ 84"#9'*+(#'( #( # &3)('2 *4 5&" # 42"*&(#( (* >"( (2"&" "11"'(&- A2DR

11.Part VII: Voltage and Current



.- W:*&" (2" &3)('2 #+$ +*(" (2" :*3 84)>2(+"&& *1 (2" _/B*:( 85:8 3)(2 (2" . .`?/B*:('"::- O*(2)+> 5+5&5#:a (2#(b& 6#4 1*4 (2" '*54&"-

Inductor, L

6-voltBulb

1-1/2 VoltCell

(a)Fig. 8

Bulb

L

(b)

switch

!"# %&'& ()! *+ '


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?- S6"+ (2" &3)('2 &:*3:D #+$ +*(" (2" 84)>2(+"&& #& (2" '*+(#'( )& 84*9"+- !"6"#( (2)&#'()*+P (2)& ()G" :"(()+> (2" &64)+> #'()*+ &+#6 (2" &3)('2 *6"+- A2#( $*"& (2"4"&5:()+> 84)>2(+"&& (":: D*5 #8*5( (2" B*:(#>" )G64"&&"$ #'4*&& (2" 85:8R ;76:#)+

)+ ("4G& * E = ! L

di

dt = ! L

" i

" t .

0- ;7#G)+" (2" ')4'5)( $)#>4#G- A2"+ (2" &3)('2 )& *6"+"$P (2" '*::#6&)+> G#>+"()'N)":$ *1 (2" )+$5'(*4 K#+ )4*+/'*4" '*):L '5(& #'4*&& 3)4"& )+ (2" '*): )+$5')+> '544"+(-A2#( 6#(2K&L #4" #B#):#8:" (* (2#( '544"+(R

,- A2D )& )( )G64#'()'#: (* 5&" #+ *4$)+#4D ./.`?/B*:( 85:8 3)(2 (2" ./.`?/B*:( 8#(("4D)+ # ')4'5)( *1 (2)& $"&)>+R

12.Part VIII: Direction of Current


0-350 VoltPowerSupply

Electromagnet

Neon GlowBulb

(a) Fig. 9

Bulb

L

(b)0-70 Volts

switch

V+ (2)& 85:8 (2"4" #4" (3* &"G)')4'5:#4 ":"'(4*$"& )+ >#&"*5& +"*+- E2" +">#()B"":"'(4*$" >:*3&P 64*B)$)+> # ':5" (* (2" 6*:#4)(D #+$ $)4"'()*+ *1 (2" '544"+( N:*3-K(2" >#& )& +"*+a )( MN)4"&M #( #8*5( c] B*:(&-L


.- A)(2 (2" B*:(#>" '*+(4*: &"( #( H"4*P (54+ *+ (2" 6*3"4 &566:D- U*:$)+> (2" &3)('2':*&"$P 4#)&" (2" B*:(#>" >4#$5#::D 5+(): (2" ":"'(4*$" \5&( >:*3&a (2)& )& )+ (2"+")>28*42**$ *1 c] B*:(&-

!"# %&'& ()! *+ 0


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?- A2):" +*()+> 32)'2 ":"'(4*$" )& >:*3)+>P *8&"4B" (2" 85:8 #& D*5 *6"+ (2" &3)('2-A2#( 2#66"+&R

0- @"( (2" B*:(#>" &:)>2(:D 8":*3 (2" 6*)+( 32"4" (2" 85:8 >:*3& #+$ 4"6"#( @("6 ?-;76:#)+ #>#)+ 3)(2 4"1"4"+'" (* (2" G" "d5#()*+-

e5&( #& )+ G"'2#+)'& # &G#:: [/6*5+$ G#&& *+ )G6#'( K ! p = F ! t L G#D 4"64"&"+( #+ #B"4#>"

1*4'" *1 G#+D (*+& *B"4 (2" &G#:: ()G" )+("4B#: )+B*:B"$P &* G#D # .?/B*:( 8#(("4D $":)B"4 #$#G#>)+> M9#4#(" '2*6M 65:&" *1 25+$4"$& *1 B*:(& )+ # ')4'5)( (2#( '*+(#)+& )+$5'()B"":"G"+(&- f"+"4 $)*$"& #4" 6:#'"$ #'4*&& (2*&" 6#4(&- E2" #G6:)N)"4 )+ # (4#+&)&(*4)H"$)>+)()*+ )& &54" (* 2#B" # f"+"4 $)*$" 6:#'"$ #'4*&& *+" *4 G*4" (4#+&)&(*4& )+ (2" ')4'5)(-

E2" '*): )+ #+ #5(*G*8):" )+B*:B"& 8*(2 &":1/)+$5'()*+ #+$ G5(5#: )+$5'()*+- E2" G#9"/84"#9 '*+(#'( #( (2" 4*(*4 4"&5:(& )+ 2)>2/B*:(#>" 65:&"& )+ (2" 64)G#4D '*):a (2" &"'*+$#4D'*): *1 G#+D G*4" (54+& 4"&5:(& )+ #+ *5(65( *1 []P]]]/B*:( 65:&"& 14*G (2" .?/B*:( 8#(("4D)+ (2" 64)G#4D ')4'5)(-

13.Part IX: Eddy Currents


N

S

Fig. 10

(a) (b) (c) (d)

x y

!"# %&'& ()! *+ &1


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.- V+&"4( (2" 84#&& &(4)6 K#L )+ (2" +*('2 #( (2" "+$ *1 (2" 6"+$5:5G K&"" =)>- .]L #+$ :"()( &3)+> 8"(3""+ (2" 6*:"& *1 (2" G#>+"(- O*(" )(& 6"4)*$ *1 *&')::#()*+ 8D &)G6:"

*8&"4B#()*+- E2)& &(4)6 4"64"&"+(& # :"+>(2 *1 M3)4"M 3)(2 +* 4"(54+ 6#(2 (2#( 3*5:$1*4G # ':*&"$/:**6 ')4'5)(-

?- V+&"4( # &)G):#4 &(4)6 K8L (2#( 2#& (3* 3)4" :**6& #((#'2"$ 1*4" #+$ #1(- Z>#)+P :"( (2"6"+$5:5G &3)+> #& 8"1*4" #+$ +*(" (2" 6"4)*$ *1 *&')::#()*+- E2"&" :**6& 4"64"&"+($)&'4"(" ':*&"$/')4'5)( 6#(2& 1*4 (2" '544"+( >"+"4#("$ )+ (2" &(4)6- =4*G (2"$)4"'()*+ *1 (2" G#>+"()' N)":$ #+$ (2" G*()*+ *1 &(4)6P $"("4G)+" K#( (2" G)$ 6*)+(*1 &3)+>LY

K#L (2" $)4"'()*+ *1 (2" '544"+( >"+"4#("$ )+ (2" &(4)6

K8L (2" $)4"'()*+ (2#( (2)& '544"+( (#9"& )+ (2" :"#$)+> #+$ :#>>)+> "$>"& *1(2" :**6 .c] º #3#D K#( 7 #+$ DL

Q*"& (2" G#>+"()' N)":$ >"+"4#("$ #4*5+$ (2" &(4)6 &566*4( *4 )G6"$" (2" G*()*+ *1(2" 6"+$5:5GR W*+&)$"4 (2" G" d5"&()*+ 1*4 (2" N)":$ #4*5+$ (2" 3)4" #( (2":"#$)+> #+$ :#>>)+> "$>"&- E2" 1*4'" )+ '*++"'()*+ 3)(2 32)'2 '544"+( N)":$ K)-"- #('"+("4 &(4)6 *4 #( 3)4"& #( 6"4)62"4DL )& 64"$*G)+#+( )+ $"("4G)+)+> (2" 8"2#B)*4 *1(2" 6"+$5:5G #+$ 32DR

0- V+&"4( (2" #:5G)+5G #+$`*4 84#&& 6:#(" #+$ '*G6#4" (2" $#G6)+> "11"'( *+ (2"

*&')::#()*+ 3)(2 (2" '#&"& #8*B"- E2)& 6:#(" *11"4& '*+()+5*5& ':*&"/')4'5)( 6#(2& K*4

M"$$)"&ML )+ 14*+( *1 #+$ 8"2)+$ (2" 4">)*+ (2#( )& G*B)+> (24*5>2 (2" G#>+"()'N)":$-

,- V+&"4( (2" &:*(("$ #:5G)+5G 6:#(" K$L #+$ +*(" (2" 6"4)*$ *1 *&')::#()*+- ;76:#)+-

[- A)(2 (2" 84#&& 6:#(" K'L )+ D*54 2#+$P G*B" )( 8#'9 #+$ 1*4(2 8"(3""+ (2" 6*:"& *1(2" G#>+"( (* "76"4)"+'" (2" $#G6)+> &"+()*+- O"7(P $4*6 )( 8"(3""+ (2" 6*:"& *1(2" G#>+"(- =)+#::DP &5&6"+$ )( )+ (2" 6"+$5:5G #+$ G*B" (2" G#>+"( 6#&( (2"&(#()*+#4D 6:#("- Q"&'4)8" (2" "11"'(&-

!"# %&'& ()! *+ &&


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#7-Magnetic Forces & Induced EMF 2181

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