FISICA III : LEY DE FARADAY Y LEY DE LENZ
INDICE INTRODUCCION:---------------------------------------------------------------------2 LEY DE FARADAY-----------ARADAY----------------------------------------------------------------------------------------------------------------------3 -----3
EJEMPLO: EJEMPLO: FEM Y CORRIENTE INDUCIDA EN UNA ESPIRA-----------4 ESPIRA-------- ---4
EJEMPLO EJEMPLO MAGNITUD Y DIRECCIÓN DE UNA FEM INDUCIDA-------6
EJEMPLO EJEMPLO CONCEPTUAL LA BOBINA EXPLORADORA------------------8 EXPLORADORA------------------8
EJEMPLO EJEMPLO GENERRADOR II: UN GENERADOR DE CD Y LA L A FUERZA
CONTRAELECTROMOTRIZ CONTRAELECTROMOTRIZ EN UN MOTOR----------------------------MOTOR-----------------------------1 1 EJEMPLO EJEMPLO GENERADOR III: EL GENERADOR DE CONDUCTOR CORREDIZO----------------------CORREDIZO----------------------------------------------------------------------------------------------12 -------------------12
EJEMPLO TRABAJO Y POTENCIA EN EL GENERADOR DE
CONDUCTOR CORREDIZO----------------------CORREDIZO---------------------------------------------------------------13 -------------13 LEY DE LENZ------------------------LENZ----------------------------------------------------------------------------------------------------------------1! ------1!
LOS GENERADORES COMO CON"ERTIDORES DE ENERG#A-----1!
EJEMPLO EJEMPLO CONCEPTUAL------------------CONCEPTUAL-------------------------------------------------------------------16 ---------------------16
LEY DE LENZ Y RESPUESTA RESPUESTA A LOS CAMBIOS DE FLUJO----FLUJO--------------1$ --1$
CONCLUSIONES--------------------------------------------------------------------18 BIBLIOGRAFIA-----------------------------------------------------------------------1%
FACULTAD DE INGENIERIA GEOLOGICA MINERA Y METALURGICA &'() 1
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ey de Faraday: F*** 5=5 . * +,,+* * /5+, +,./+* *5 /.*,5 ' '&+*, /*+ ,5 ,* 9.;* . **=+*, /+/.+5) *5 , * . ,.,/+*: L* 9.;* /55+; +,./+* , ., /+/.+5 +/*, &5&5/+5,* * * =5/+* /5, . /*+* .>5 . **=+* /+/.+5)
2. LEY DE FARADAY E ,5 /5, , 55 5 9/5 +,.//+0, .>5 *(,7+/5 /*+*, * *=7 ., /+/.+5) A, ,.,/+* * 9+/* ,/+* . . 5* * /* @&+,5 =+5 &+5 /5,/&5 .>5 *(,7+/5 Φ B ) P** ., ,5 '* +,H,++*
dA
, ., /*&5 *(,7+/5 d ΦB
5 *(,7+/5 '* :
B
* *=7
d ΦB =⃗ B.d A= B⊥ . dA = BdA cos ∅
D5,
B⊥
* /5&5,,
,5 '*
∅
B
&&,+/.* * * .&H/+
, ',(.5 ,
B yd A
) E .>5 F+() 2%)3 Φ B * *=7 ., '* +,H,+* * +,(* * *(,7+/5 5* @&+0, 5 '*:
∫ ⃗B . d A =∫ BdA cos
Φ B=
S+
B
⃗
∅
.,+95 5 ., '* &*,*
A
,5,/:
Φ B= B . A = BA cos ∅
L* H(.* 2%)4 &** * (* &** .5 * /.*/+0, *,+5)
F+() 2%)4
L* ley de Faraday de la Inducción */ 5 +(.+,: La fem inducida en una espira cerrada es igual al negativo de la tasa de cambio del ujo magnético a través de la espira con respecto al tiempo.
E, 55 * L F*** : ε=
−d Φ B dt
P** /5&, +(,5 ,(*+=5 ,/*+5 +,5./+ .,* /5,=,/+0, +(,5 &** * 9 +,./+* ) 2.1. EJEMLO: FEM Y CORRIENTE INDUCIDA EN UNA E!IRA
E /*&5 *(,7+/5 , 5 &55 ., /5+', * H(.* 2%)! .,+95 , /.*.+ 5,5 &5 . *(,+. +,/,* * *;0, 0.020 T / s ) E '* * &+* /5,./5* , /*&5 120 cm * +,/+* 5* /+/.+5 +,/.,5 +5 !) K) A? E,/., * 9 +,./+* * /5+, +,./+* , /+/.+5) B? S+ .+. * &+* &5 5* /* ., F+() 2%)! *+* *+*, .7 9/5 ,' 5 5 * 9 +,./+* * /5+, +,./+* 2
!OLUCION: IDENTIFICAR:
E /*&5 *(,7+/5 * *=7 .,* &+* /*+* /5,95 5+H/* /*&5 *(,7+/5) D * 95* *' .,* 9 +,./+* , * &+* &5+ ,/5,* . =*5 <.,* * +,/0(,+*? &*,5 * F***) L* /5+, (,** ,* &+* &5 * 9 <* 5* =*+* . ./*5? +,* .*,5 * +* 7/,+/* .** *,+5,) LANTEAR: Φ B= B . A = BA cos ∅ C5, * /.*/+0, &55 /*/.* .>5 *(,7+/5 .(5 .++;*5 * F*** */.5 /5, *
/.*/+0,
ε=
−d Φ B
&** +,* * 9 +,./+* .*, )
dt
D&.7 /*/.* * /5+, +,./+* . &5./ * 9 &5 +5 * */+0, ε = IR 5, R * +,/+* 5* /+/.+5 . +,/. * &+*) EJECUTAR:
A? E '* =/5+* * &+* &&,+/.* * &*,5 * &+* 5&*5 &5 . * =+/*, */+* *+*) A 5 =/5 A B 5, &**5) C55 B .,+95 .>5 *(,7+/5 * *=7 * &+* Φ B= B . A = BA cos0 =BA ) E '* A = 0.012 m /5,*, &5 5 . * ** /*+5 .>5 *(,7+/5 : 2
d ΦB dt
=
d ( BA ) dB = A dt dt
¿ ( 0.020 T / s ) ( A =0.012 m ) =2.4 × 10− V =0.24 mV 2
4
E5 *&* ., +(,5 . *, ,5 5 *,*+;*5 * 9 +,./+* ) L* /5+, +,./+* /5&5,+, : −4
ε 2.4 × 10 V =4.8 × 10−5 A =0.048 mA I = = R 5.0 Ω
B? A /*+* * .,* &+* /* *+* *+*, * +,/+* */ . (*,) L* F*** ,5 +&+/* * +,/+* /+/.+5 ,+,(.,* 95* &5 5 . * 9 +,./+* ,5 /*+*) P5 * corriente ' ,5 (, * /.*/+0,
ε I = R
) S+ * &+* .=+* /* ., *+*,
&9/5 +,/+* +,H,+* * /5+, +,./+* ' +(.* * /5 *., /.*,5 .=+* &, .,* 9) E* +.*/+0, *,'5(* * * .,* ** *+** /.* +,* ,5 7,
/5,/** * ,**: * .,* 9 &, &5 ,5 . /5+,) E"ALUAR:
E, /'/.5 /5,=+, =+H/* * /5,+,/+* * .,+*) * ./* *,* */5 .,* 5=* . +5 * * */+0, * 9.;* *(,7+/* F =q v × B * .,+* /*&5 *(,7+/5 5, * * 9.;* +=++* , * .,+* ⃗
/*(* &5 =5/+*: .,+*
.>5
m
=( 1 N )( 1 C . ) ) E, /5,/.,/+* * s
1 T
*(,7+/5
&.,
@&*
/55
( 1 T ) ( 1 m )= 1 N . s . m * ** /*+5 .>5 *(,7+/5 /55 C 2
1 N .
m J =1 =1 V C C
) A * .,+*
.+ * /.*/+0,
ε=
−d Φ B dt
d ΦB dt
) T*+7, * . /5* . *
.,+* .>5 *(,7+/5 <?: .
1 V
=1
Wb s
=5 /55 5
2
1 T . m =1 Wb
&5 5
)
Dirección de la #e$ inducida
L* +//+0, .,* 9 5 /5+, +,./+* /*/.* /5, * /.*/+0, *,+5 /5, *(.,* (* ,/+* &** 5 +(,5) E &5/++,5 +(.+,: 1) DH,* .,* +//+0, &5++=* &** =/5 '* 2) A &*+ * +//+5,
A
/*+5
dt
)
/*&5 *(,7+/5
+, +(,5 .>5 *(,7+/5 d ΦB
A
ΦB
B
. **
) L* H(.* 2%)6 &,* =*+5 >&5)
3) D+, +(,5 * 9 5 /5+, +,./+*) S+ .>5 //+, *,* .
d ΦB dt
&5++=* ,5,/ * 9 5
/5+, +,./+* ,(*+=* + .>5 //+,
,5,/
d ΦB dt
,(*+=* * 9 5 /5+, +,./+*
&5++=*) 4) P5 +5 +, * +//+0, * 9 5 /5+, +,./+* /5, * *.* . *,5 /* D5 5 5 * *,5 /* *5 =/5 A /5, &.(* , +//+0, ⃗
A
) S+ * 9 5 /5+, +,./+* , /+/.+5 positiva ' , * +* +//+0, 5 5 5*5) S+ * 9 5 /5+, +,./+* negativa ,/.,* , +//+0, 5&.*)
S+
F+() 2%)6+7,+/* .>5 =*+* , * +, .,* 5+,* /5, N &+* +* ** * *=7 /** &+* * ** 5* /*+5 * *=7 5* * &+* N =/ ' (*, . &** .,* 5* &+* )S+ QB .>5 * *=7 /** &+* * 9 5* .,* 5+,* /5, N &+*
-N
dΦ B dt
<2%)4?
C55 =+5 , * +,5.//+0, /*&.5 * 9 +,./+* &*, ., &*& ,/+* , * (,*/+0, * ,(* 7/+/* &** .5 /5/+*) "*+5 5 >&5 . +(., @&5*, +9, 755 &** (,* 9 &5 +5
5=++,5 ., /5,./5 /5, &/5 * ., /*&5 *(,7+/5 5 . * .(* * ., .>5 /*+*, * *=7 ., /+/.+5)
.2.EJEMLO MA%NITUD Y DIRECCI&N DE UNA FEM INDUCIDA S /55/* .,* 5+,* ** . /5,+, ! &+* /+/.* /5, *+5 4) / , 5 &55 ., /5+', (*, 5, /*&5 *(,7+/5 .,+95 +, ., ',(.5 6 5 /5, &/5 * &*,5 * 5+,* )E /*&5 ++,. * *;0, )2 T) C.' 5, * *(,+. +//+0, * 9 +,./+* !OLUCI&N IDENTIFICAR: N.* +,/0(,+* * 9 +,./+* &5 ., .>5 *(,7+/5 =*+* * *=7 * 5+,*) E .>5 =** +5 * . * *(,+. /*&5 *(,7+/5 ++,.) LANTEAR: S +( . * +//+0, =/5 '* A * * . 5=* , * H(.* 2%)$)C5, * //+0, * (5* . ++* * * * H(.* 2%)6)E* H(.* ,5 *.** * +,* * +//+0, * 9 +,./+*) EJECUTAR: E /*&5 *(,7+/5 .,+95 , 5* * &+* &5 5 .
&5+ /*/.* .>5 /5, * /.*/+0, <2%)2?: QBBA /5V 5, V35)E, * @&+0, * ,+/* /*,+* . /*+* /5, &/5 * +&5 * *(,+. B /*&5)
CUIDADO: R/. /55 H, V) T* =; .=5 ,*5 .++;* V65 , &5*) S+ * 9. /. . V ',(.5 , B
,5 ,
B
A
&*,5 * &+*)
F+() 2%)$ L* ** /*+5 .>5
d ɸB
<B? A /5W) E, ,.5 &5* B -)2 T A <)4? 2)!32 &5 5 .
dΦ B dB 5 2 2 dt dt A /5 3 <-)2 T?<)!3 ?<)866? -8) T)
-8)$1@
−4 10
L* 9 +,./+* , * 5+,* N ! &+* (, * /.*/+0, <2%)4?) ¿ ε =− N
dΦ B =−(500)¿ -8)$1@ dt
−4 10
? )43! "
O= . * &.* &5++=5) E5 +(,+H/* . /.*,5 *&.,* &.(* /5 , * +//+0, =/5 '* A <35 &5 *+* /*&5 *(,7+/5 B ? * +//+0, &5++=* &** ε /5&5, * * 5 5 5*5 * *,5 /*) D * . , >&5 * 9 ,(* * +* +//+0, 5&* /5, * H(.* 2%)6?)S+ , * H(.* 2%)$/+*5 * 5+,* *5 +;.+5 , * +//+0, A * 9 +* , ,+5 5*+5) ⃗
E"ALUAR: S+ /5,/*, 5 @5 ** >.,5 * +//+0, , * /5+, , * 5+,* +* * +* . * * 9 /+ , ,+5 5*+5 =+,5 * +;.+* * 5+,*) U,* /5+, , ,+5 5*+5 *((* .>5 *(,7+/5 * *=7 * 5+,* , * +* +//+0, . .>5 /5+', &5 5 . +, * 5&5, * * ++,./+0, .>5 5*) .'. EJEMLO CONCETUAL LA (O(INA E)LORADORA
U,* 95* &'/+/* + * +,,+* ., /*&5 *(,7+/5 .* .,* 5+,* &.* N &+* /5, =*,*5 /5&*/5 *** 5+,* @&5*5*) I,+/+*, * 5+,* '* A /55/* *,* . . =/5 '* A *+,*5 /5, ., /*&5 *(,7+/5 *(,+. B) L.(5 * 5+,* */ (+* /5, *&+; ., /.*5 =.* , 5,5 * . +'5 5 +, */* * 5+,* /*&5 '&+*,) E@&+. /05 &. .* +&5++=5 &** + =*5 B) !OLUCI&N:
A &+,/+&+5 .>5 * *=7 * 5+,* ɸ B NBA /.*,5 * 5+,* */ (+* 5 */* /*&5 .>5 ++,. '&+*, NBA * /5) M+,* .>5 ++,. * .,* 9 +,./+* 5,',* , ., /+/.+5 @,5 /5,/*5 * * 5+,*) L* ** /*+5 .>5 * *=7 * 5+,* &5&5/+5,* * * /5+, 5 ** .>5 /*(* &5 5 . 9'/+ 5* .
/*+5 5* .>5 &5&5/+5,* * * /*(* 5* . . &5 /+/.+5) S &. /5,.+ ., +,.,5 . +* * /*(* 5* * &*+ 5 5, =*5 B) .'. EJEMLO %ENERADOR I: UN ALTERNADOR !IMLE
L* H(.* 2%)8 .* .,* =+0, ,/+* ., *,*5 ., +&5++=5 . (,* .,* 9) S */ (+* .,* &+* /*,(.* /5, *&+; *,(.* /5,*, *5 > . +,+/*) E /*&5 *(,7+/5 B .,+95 /5,*,) E, 5,5 Φ =0
) D+, * 9 +,./+*)
!OLUCI&N: IDENTIFICAR: D ,.=5 * 9 <* =*+* ./**? &5./5 ., .>5 *(,7+/5 =*+*) S+, *(5 , * +.*/+0, /*&5 *(,7+/5 B /5,*, .>5 /*+* &5. * +//+0, A
/*+* * (+* * &+*)
2*.+
*? D+*(** ., *,*5) U,* &+* /5,./5* (+* , ., /*&5 *(,7+/5 5 . &5./ .,* 9) L* /5,@+5, , /** @5 * &+* /+/.+5 @,5 9/*, &5 +5 ., *,+5 /5/5 , @5) E +* Φ =wt =¿ %5 ) +.* &** 5,5 , . ',(.5 ? G*H/* .>5 * *=7 * &+* * 9 .*, , * +,* * * 5 *(5 * &5+/+5, /5&5,+, * &+* .*, .,* 5*/+0, /5&*)
F+() 2%)8
LANTEAR: * H(.* 2%)8* +.* * +//+0, =/5 '*
) O= . /5,95 * &+* (+* A,(.5 , *.,* * ., +5 /5,*,)
A
A B
EJECUTAR: ,.=5 /*&5 *(,7+/5 .,+95 , 5* * &+* &5 . 9'/+ /*/.* .>5 *(,7+/5) L* ** /*+5 A,(.5 +(.* * * *&+; *,(.* * &+* &5 5 . &55 /++ ) P5 5 *,5)
B BA /5 BA /5 ) L* +=** /5 <? /5 - , ) P5 5 . (, * F*** [/.*/+0, <2%)3?\ * 9 +,./+* Ԑ=
−dɸB dt
=BA sen ɯ t
E"ALUAR: * 9 +,./+* E =*+* , 95* +,.5+* /5, &/5 * +&5 <=7* * H(.* 2%)8?) C.*,5 &*,5 * &+* &&,+/.* * B < 5 18 5? B */*,;* . =*5 '@+5 ,+5) E 5 5,5 . ** +,*,',* /*+5 +(.* * /5 E /5) A++5 E '@+* , =*5 *5.5 /.*,5 &*,5 * &+* &**5 * B < % 5 2$ 5? B ' /*+*,5 /5, * '@+* *&+;) P5 +5 5=* . * 9 +,./+* ,5 &, * 95* * &+* +,5 55 . '*) C55 E +/*, &5&5/+5,* * * B *(.,5 */05 .++;*, * 9 , .,* 5+,* (+*5+* &** + * *&+; 5*/+0,) O5 +&5++=5 *&5=/*, * 9 * /* &** + /*&5 *(,7+/5)
P55 .++;* *,*5 /55 9., 9 , ., /+/.+5 @,5 &*,5 5 *,+5 /5/5 . (+*, /5, * &+* /55 +.* , * H(.* 2%)8*) L5 *,+5 +;*, /5,* .,5 /5,*/5 H>5 **5 /5+* . ', /5,/*5 * * +,* @+5 * ) /55 * 9 =*+* , 95* +,.5+* *
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
F+() 2%)% .,. EJEMLO %ENERRADOR II: UN %ENERADOR DE CD Y LA FUER-A CONTRAELECTROMOTRI- EN UN MOTOR
E *,*5 >&5 2%)4 &5./ .,* 9 . =** 55 +,.5+* &5 5 (,* .,* /5+, *,*) S &. .++;* ., .* ++* &** 9*+/* ., (,*5 /5+, +/* ? . &5.;/* .,* 9 . +& ,(* +5 +(,5) E, * H(.* 2%)1* +.* ., &55+&5 (,*5) E *(5
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
F+() !OLUCION IDENTIFICAR: &5 5 . &/* * * &+* (+*5+* * +.*/+0, * +* . * >&5 2%)4 @/&5 . *5* * N &+* **) S+, /5,.*5 * 9 *,** , =*5 &5++=5 ,(*+=5 ,* ., =*5 +5 /5 &5 2%)4 +,** .,* @&+0, &** =*5 +5 &>** * *&+; 5*/+0, <,.* +,/0(,+*? LANTEAR: &*,*+,5 +5 . >&5 2%)4 EJECUTAR: * /5&**/+0, * H(.* 2%)8 * 2%)1 .* . * 9.;* /5,* /55+; 55 *, 55 =*5
*5.5 * 9 /*/.** &** *,*5 , >&5 2%)4 .+&+/** &5 +5 N &+* , * 5+,* /55 , * /.*/+0,<2%)4?: |Ԑ|= N ɯ BA|sen ɯ t |
P** 5, * 9.;* /5,* /55+; +* .+. ], ] &5 . =*5 +5) E =*5 +5 * 9.,/+0, ,5 ,/.,* /5, * +,(*/+0, , 5 +5 /+/5 * T2 &** .(5 +=++ .*5 , +&5 *,/.+5 ) .*, +5 /+/5 * 9.,/+0, ,5 &5++=* &5 5 . ], ], +, π / ɯ
∫ sen ɯt dt
<], ]?
0
π / ɯ
2
π
O //* )64) E,5,/ * 9.;* /5,* /55+; +* Ԑ
2 NɯBA
π
L* 9.;* /5,* /55+; &5&5/+5,* * * *&+; 5*/+0, ) * &>* 5+,:
π Ԑmed 2 NBA
π ( 112 V )
(
)(
)(
2 500 0.200 T 0.100 m
2
)
1$6 *
E"ALUAR: * 9.;* /5,* /55+; +* +/*, &5&5/+5,* * ) * 95* /.*,5 ,5 * * *&+; 5*/+0, ,5 ' * 9.;* /5,* /55+; *5 * &5+++* .* 55) .. EJEMLO %ENERADOR III: EL %ENERADOR DE CONDUCTOR CORREDI-O
L* H(.* 2%)11 .* ., /5,./5 , 95* U , ., /*&5 *(,7+/5 .,+95 B &&,+/.* * &*,5 * H(.* ++(+5 */+* * &'(+,*) C55/*5 .,* =*+* * /5, 5,(+. L , 5 5 *;5 /5,./5 &** 95* ., /+/.+5 5=5 * =*+* */+* * /* /5, =5/+* v /5,*,) E5 ,./ .,* 9 /5+, . * *;0, &5 * . +&5++=5 ** (,*5 /5,./5 /5+;5) D+, * *(,+. +//+0, * 9 +,./+* .*,) ⃗
⃗
F+()
2%)11 (,*5 /5,./5 /5+;5) T*,5 /*&5 *(,7+/5 B /55 '* A =/5+* ', ++(+5 */+* * H(.*) E *.,5 , .>5 *(,7+/5 *.*5 &5 ., +,/,5 '*? +,./ * 9 * /5+,)
!OLUCION IDENTIFICAR: .>5 *(,7+/5 /*+* &5. '* * &+*++** * * /* &5 * =*+* 0=+- ' *.,*,5) L* =*+* . ./*5 * 9 Ԑ +,./+* * &+* , @&*,+0,) LANTEAR: /*&5 *(,7+/5 .,+95 5 '* * &+* &5 5 . ,.=5 /*/.* .>5 *(,7+/5 &*,5 ɸB = BA cos ɸ) S +( . =/5 '* A *&., +/5
*/+* &*,5 * +.*/+0, , * +* +//+0, . B ) C5, * //+0, .,* 9 &5++=* ' *.* . ' ++(+* , ,+5 5*+5 *5 * &+*) ⃗
EJECUTAR: /55 B A *&.,*, , * +* +//+0, *,(.5 BA) L* *(,+. /*&5 *(,7+/5 B /5,*, &5 5 . * 9 +,./+* : Ԑ=
−d ɸ B dt
=−B
dA dt
P** /*/.* A 5=* . , 5,5 * =*+* /5+;* &*;* .,* +*,/+* =
Lv dt =− BLv dt
E +(,5 ,(*+=5 ,5 +,+/* . * 9 ' ++(+* , ,+5 *,+ 5*+5 *5 * &+* * +(.* . * /5+, +,./+* /55 .* , * H(.*) E"ALUAR: 5= . * 9 /5,*, + * =5/+* v * =*+* /5,*,) E, /*5 (,*5 /5,./5 /5+;5 */* /55 ., (,*5 /5+, +/*) N5 ., +&5++=5 . &'/+/5 * . * =*+* , *(, 5,5 ⃗
.= ' *' /5,./5 , 95* U /5,*/5 &+ /5, 5 . * /5+, /*) ./. EJEMLO TRA(AJO Y OTENCIA EN EL %ENERADOR DE CONDUCTOR CORREDI-O
E, (,*5 /5,./5 /5+;5 >&5 2%)6 * ,(* ++&* , /+/.+5 +5 * . +,/+*) S* R * +,/+* /+/.+5 5,+.+5 &5 /5,./5 /5+;5 /5,./5 , 95* U . /5,/* 5 @5 /5,./5 /5+;5? , ., &.,5 *5 5=++,5 /5,./5 /5+;5) D. . * ** * * . ++&* ,(* , /+/.+5 @*/*, +(.* * * ** * * . 9/.* **>5 &** &*;* * =*+* * *=7 /*&5 *(,7+/5) !OLUCION IDENTIFICAR: * =*+* ./** 5, * ** * * . ++&* ,(* . *+;* **>5) E5 +(,+H/* . **>*5 /5, /5,/&5 &5,/+*) L* ,(* ++&* , /+/.+5 &5. * +,/+*: &** /++ 5 ,/+*5 +*) S .+ **>5 &** 5= * =*+* &5. * .,* /5+, +,./+* . . * *=7 .5) E /*&5 *(,7+/5 >/ .,* 9.;* 5 * =*+* /5,./5* /5+, .+, &.>* * =*+* ,' . 9/.* **>5 , /5,* * 9.;*) 2*.12 * 9.;* *(,7+/*
⃗xB F = I L ⃗
. */.* 5 * =*+*
+5 * * /5+, +,./+* =* */+* * +;.+* 5&.* *
v ⃗
F+() LANTEAR: , >&5 2%)6 /*/.0 * 9 +,./+* E /+/.+5) L* /5+, I , /+/.+5 +(.* * =*5 *5.5 E +=++5 , * +,/+* R * ** * * . ++&* * ,(* , * =*+* P ++&** I2R) L* 9.;* *(,7+/* 5 * =*+* F = I L x B =/5 L *&.,* * 5 *(5 * =*+* , *
+//+0, * /5+,) L* H(.* 2%)12 .* . * 9.;* 5&.* * * =5/+* * =*+* &5 5 . &** *,, 5=++,5 *&+/* .,* 9.;* +(.* *(,+. , * +//+0, 5=++,5 * =*+* < /+ , +//+0, v ?) L* ** /5, . 9/.* **>5 +(.* * &5./5 * 9.;* *&+/** &5 * *&+; * =*+* P *&+/** Fv ) ⃗
EJECUTAR: &+5 /*/.** P++&**) D */.5 /5, >&5 2%)6 - BLv ) E, /5,/.,/+* * /5+, , * =*+*
|Ԑ|
I =
R
=
BLv R
Y * ** ++&*/+0, ,(*
( )
2
2
d!s!"#d# = I R =
2
2
BLv B L v R = R R
2
P** /*/.* P++&** &+5 +,* * *(,+. F = I L x B ) C55 L B 5, &&,+/.* * *(,+. 2
2
BLv B L v F = ILR= LB = R R
P5 5 *,5 * ** /5, . * 9.;* *&+/** *+;* **>5 2
2
B L v #"$!c#d# = Fv = R
2
E"ALUAR: L* ** * * . *+;* **>5 @*/*, +(.* * * ** * * . * ,(* ++&* , * +,/+*
.0. LO! %ENERADORE! COMO CON"ERTIDORE! DE ENER%A
E >&5 2%)$ .* . (,*5 /5,./5 /5+;5 ,5 &5./ ,(* 7/+/* * ,** * ,(* * .+,+* /.*.+ /.&5 . >;* * 9.;* &** *,, * =*+* , 5=++,5) T55 5 . */ (,*5 /5,=+ * ,(* * .,* 95* +9,) L* +(.** , * ** /5, . .+,+* ,(* /',+/* * (,*5 * ** /5, . &5./ ,(* 7/+/* /.& &** 55 5 +&5 (,*5) E5 /+5 , &*+/.* &** *,*5 /+5 , >&5 2%)4) +, .,
*,*5 5 , * =*+* /5,./5 , 95* U ., (,*5 /5,./5 /5+;5) S+ +,/.*, * 9/5 * /5,=*/+0, * ,(* *,** . * ,(* &+* &5 * 9+//+0, ,5 .=+* +&5,+ &** /5,=+ , ,(* 7/+/*) E, 5 (,*5 * * 9+//+0, *,+, , ,+5 &** . &5/5 /5,=+0, ,(* * 5 ' H/+, &5+?)
'. LEY DE LENL* L,; ., 755 *,*+=5 /5,=,+, &** +,* * +//+0, .,* /5+, 5 9 +,./+*) L* L,; ,5 ., &+,/+&+5 +,&,+, &. 5, * F***) S+& * 5 +5 .*5 . * (* 5 +(,5 . &,*5 , */+0, /5, * F*** &5 * ,.5 ' 9'/+ .*) L* L,; *+7, *.* * ,, *,* +,.++=* 5 ++,5 9/5 * +,.//+0, &*& * /5,=*/+0, * ,(*) )F)E) L,; <184-186!? 9. ., /+,H/5 .5 . &5.>5 95* +,&,+, ./5 5 /.++,5 F*** ,) L* ley de Len */ 5 +(.+,: ^L* +//+0, /.*.+ 9/5 * +,.//+0, *(,7+/* * . 5&5, * * /*.* 9/5_ L* /*.* &. ., .>5 /*+*, * *=7 ., /+/.+5 H>5 +5 * ., /*&5 *(,7+/5 =*+* ., .>5 . /*+* &5 5=++,5 5 /5,./5 . /5,+., /+/.+5 5 /.*.+ /5+,*/+0, 5 *,+5) S+ .>5 , ., /+/.+5 H>5 /*+* * /5+, +,./+* */ ., /*&5 *(,7+/5 &5 +*) D,5 '* ++** &5 /+/.+5 /*&5 5&.5 * /*&5 5+(+,* + +,/,* &5 +, * +* +//+0, . /*&5 5+(+,* + ++,.) E /+ * /5+, +,./+* 5&5, * /*+5 , .>5 * *=7 /+/.+5 <,5 * .>5 , ?) S+ /*+5 .>5 * 5=++,5 5 /5,./5 * +//+0, * /5+, +,./+* , /5,./5 , 5=++,5 * . * +//+0, * 9.;* *(,7+/* 5 /5,./5 5&.* * * +//+0, . 5=++,5) A 5=++,5 /5,./5 . &5=5/5 * /5+, +,./+* ,/.,* 5&5+/+0,) E, 55 5 /*5 * /5+, +,./+* ** &=* statu quo 5&5,+7,5 * 5=++,5 5 * ., /*+5 .>5) L* L,; *+7, */+5,* +/*, /5, * /5,=*/+0, * ,(*) S+ * /5+, +,./+* 9.* , +//+0, 5&.* * * . +,+/* * L,; * 9.;* *(,7+/* 5 * =*+* *
*/** */+* .,* *&+; +& //+, +, .,* 9., @,* ,(* *., /.*,5 * ,(* 7/+/* ++&** , /+/.+5) E5 * .,* /** =+5*/+0, * /5,=*/+0, * ,(* ,5 5/. , * ,*.*;*) .1. EJEMLO CONCETUAL
E, * H(.* 2%)13 * ., /*&5 *(,7+/5 .,+95 B * *=7 * 5+,*) L* *(,+. /*&5 =* , *.,5 * 9 +,./+* .*, 5/*+5,* .,* /5+, +,./+*) C5, * , * L,; +, * +//+0, * /5+, +,./+*)
!OLUCI&N S(, * L,; * /5+, +,./+* &5./+ ., /*&5 *(,7+/5 &5./+ ., /*&5 *(,7+/5 B !nd%c!d& D,5 * 5+,* /.* +//+0, */+* **>5 , 5&5+/+0, * /*+5 , .>5) C5, * (* * *,5 /* &** * +//+0, /*&5 *(,7+/5 &5./+5 &5 .,* &+* ⃗ /+/.* B !nd%c!d& ,' * +//+0, ** + * /5+, +,./+* . /55 +,+/* , * H(.* 2%.13) L* H(.* 2%)14 .* =*+* *&+/*/+5, * L,; * * +.*/+0, ++* ., +', . .= //* .,* &+* /5,./5*) E, /** .,5 5 /.*5 /*5 . +.*, * /5+, +,./+* &5./ ., /*&5 *(,7+/5 &5 +* , .,* +//+0, . 5&5, * /*+5 .>5 * *=7 * &+* +5 * 5=++,5 +',)
.2. LEY DE LEN- Y RE!UE!TA A LO! CAM(IO! DE FLUJO
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
,. CONCLU!ION: E, * +,=+(*/+0, **>5 `/5*(,+5` + /.,* . ./5 *&**5 7/+/5 . +,/.5 ,5 , * /** 9.,/+5,*, (*/+* * 9,0,5 . * +5 *, .+*5 &5 *,5 *5 . /** =; &,*, ,.=5 *=*,/ , * /,55(* , * /5.,+/*/+5, (*/+* * /5*(,+5) E, **>5 &. * /.,* 5 . +(,+H/* 9,0,5 /5*(,+5 . .5 . +5+* 5 /+,H/5 . 5 *, .+*5 &5 *5) S &. *&/+* /55 5 9,0,5 /55 * /+/+* *(,+5 .,, 95*,5 /,5 ,.* +,=+(*/+0, /55 ., +& 5,+5 + ,.* /** &. /5,, * /+,/+* .+** 5 . +(,+H/* . 5, +5 * 9+/* =* * * * /5, *(.,5 . +& 9,0,5) L* =+* , * +* ,5,* * * 9+/* * * . ,5 @&+/* 5 +9, 9,0,5 . ./, * ,.5 *5) E *.5 +,./*,/+* +,&,+, =5*> 5 * +,,+* /5+,) E' +,** &5 * (5* * 5+,* * &5&+* *(,7+/* ,/5) L* +,.//+0, 5/. 5*, /.*,5 /5,./5 .= , ',(.5 /5 /5, &/5 * * +//+0, /*&5 *(,7+/5) E 5=++,5 ,/*+5 &** . &5.;/* * +,.//+0, &5 ., 5=++,5 *+=5 , /5,./5 /*&5 *(,7+/5) D * 95* ., /*&5 *(,7+/5 , @&*,+0, /5&+0, &. /* /5, .,* /5+, * *=7 ., /* 5 ., /5+',) D*5 . * /5+, /5+', *.,* ./ . /*&5 *(,7+/5 @&*, /5&+ <* ,* 9.;* .=, */+* **, */+* *'?) E /*&5 , 5=++,5 &. +,./+ .,* /5+, , ., +5 H>5 //*,5) P** &5./+ ., .>5 /5+, , /.*.+ /+/.+5 7/+/5 ,/*+* .,* 9., 9.;* /55+;) C.*,5 */ 5/+* ., /5,./5 , ., /*&5 *(,7+/5 .>5 /5+, , /5,./5 /*+* ,+5 *,* =/ /55 5 */ 5=++,5 9+/5 /5,./5)
!) BIBLIOGRAFIA: F++/* U,+=+*+* 12=*) E+/+5,
S* Z*,a "5) 2