GENERACION ELECTRICA CON EL CAMPO MAGNETICO TERRESTRE
Ing. Humberto Porta Caldera Ing. Mauricio Porta Mora
San José, Costa Rica
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MAURICIO PORTA MORA Y HUMBERTO PORTAR PORTAR CALDERA
GENERACION ELECTRICA CON EL CAMPO MAGNETICO TERRESTRE / Hu!"#to Po#ta C$ % Mau#icio Mau#icio Po#ta M$ & "#a$ E'ici(n San José, José, Costa Costa Rica$ Rica$ )*&+ Painas, &- . & c$ I0ust#acion"s1 $ Dis"2o G#34ico % Dia#aaci(n1 H$ Po#ta C$ % M$ Po#ta M$ )*&+
5u"'a tota0"nt" 6#o7i!i'o uti0i8a# "sta in4o#aci(n tota0 o 6a#cia0"nt" 6a#a usa#0a "n 0a "n"#aci(n '" "0"ct#ici'a' uti0i8an'o "0 ca6o anético '" 0a ti"##a, sin 0a auto#i8aci(n 6o# "sc#ito '" 0os auto#"s$ Est" 0i!#o no 6o'#3 s"# #"6#o'uci'o ni tota0 ni 6a#cia0"nt", "n ninuna ninuna 4o#a, sin "0 "0 6"#iso 6o# "sc#ito '" 0os auto#"s$ To'os 0os D"#"c7os R"s"#9a'os$
:):
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MAURICIO PORTA MORA Y HUMBERTO PORTAR PORTAR CALDERA
CONTENIDO Pag. ! INTROD"CCION
4
# ! PRINCIPIOS $ASICOS "TILI%ADOS
&
' ! DE(INICION DE "NIDADES
) ! CAMPO MAGNETICO TERRESTRE
*
+ ! CONSIDERACIONES CONSIDERA CIONES PARA PARA GENERACI,N GENERACI, N ELECTRICA CON EL CAMPO MAGNETICO TERRESTRE #+ +. ! CON(IRMACION DE GENERACION #ELECTRICA CON GEOMAGNETISMO GEOMAGNETI SMO * ! RE(ERENCIAS
: ; <
''
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MAURICIO PORTA MORA Y HUMBERTO PORTAR PORTAR CALDERA
INTROD"CCION/ Tanto la Teoría oría Cuánti Cuántica ca como como la Mecán Mecánica ica Ondu Ondula lato tori ria, a, han han demo demost stra rado do tant tanto o teór teóric ica a como experimentalmente , que la energía se transmite
en
el
espacio
en
cantidades
discretas, discretas, finit finita a y definida. definida. Estos paquete paquetess de energía, conocidos como Cuantum de cción se han designado con la letra !h" y se conocen con el nom#re de Constante de $lanc%, en honor de su descu#rir, Max Max $lanc%. Experimentalmente se ha determinado el &alor de la Constante de $lanc% !h"' h = 6.62607 x 10 a la – 34 Julios x Seg. ::
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El cuantum de acción corresponde a la energía de una sola partícula. Conforme con la Teoría Electromagn(tica de )oren* y la de Max+ell, el fluo magn(tico se representa representa por por líneas líneas de fuer*a fuer*a magn(tic magn(tica. a. El n-me n-mero ro tota totall de líne líneas as de fuer fuer*a *a crea crean n un campo
magn(tico
por
unidad
de
área
perpendicular, al que se le llama fluo magn(t magn(tico ico.. )a unidad unidad del fluo fluo magn( magn(tic tico o es una sola línea de fuer*a. )os )os pol polos del del cam campo magn( agn(titico co terre errest stre re corre corresp spon onde den n a dos dos -nic -nicos os punt puntos os so#r so#re e la superficie de la tierra donde el campo magn magn(t (tic ico o es &ert &ertic ical al..
)as )as coord coorden enad adas as
geográfica del polo orte son' /01 latitud orte orte y 231 longit longitud ud Oeste. Oeste. )a magnitud magnitud del campo campo magn(tico en la superficie de la tierra &aría entre 0.45 a 0.35 6aus y se puede considerar :+:
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como el campo magn(tico creado por un dipolo magn(tico inclinado unos 701 con respecto al ee de rotación de la tierra. En Costa 8ica en latitud muy ceca a 701 orte, el fluo magn(tico &ertical se encontró el &alor de 9 x 70 a la : 5 ;e#er< metro cuadrado, utili*ando un magnetómetro T=$6' M> : 98. En los siguientes capítulos se presentan los $rincipios, ?efiniciones @ásicas y Ecuaciones con las que se formulan los análisis y resultados que conforman este tra#ao.
:=:
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# ! PRINCIPIOS $ASICOS "TILI%ADOS
El desa desarr rrol ollo lo de este este tra# tra#a ao o se #asa #asa principalmente
en
los
principios
las
sig siguientes
de
conceptos
y
teorías
amplia ampliamen mente te recono reconocid cidas as y apro#a apro#adas das como fundamento de la Ciencia actual' A Teoría Cu Cuántica, A Mecán ecániica Ondu Ondullator atoriia. A Constante de $lanc% BCuantum de cción. A Teoría oría Elec Electr trom omag agn( n(titica ca,, Ecua Ecuaci cion ones es de Max+ell. A Teorí oría Elec Electr trom omag agn( n(titica ca de 6aus 6ausss y Duer*a Magn(tica de )oren*. A Teoría oríass del del Camp Campo o Magn Magn(t (tic ico. o. A Teoría oríass del del Camp Campo o El(c El(ctr tric ico. o. :>:
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A $rincipios
de
nducción
ElectroA
magn(tico. A )ey )ey de @iot @iot.. Bnd Bnduc ucci ción ón elec electr trom omag agn( n(AA tica en una Espira El principio #ásico utili*ado es el concepto del Cuantum de cción el cual esta#lece que la Energía se transmite en el espacio de manera discreta en cantidades definidas y constantes, por paquetes de energía en forma discontinua con una frecuencia entre los / y 79 ciclos por segundo para efectos del campo magn(tico. magn(tico. El &alor de cada cuantum de acción es' h F 3.3430/ x 70 a la A9G en HuliosA>eg., y de h F G.795/ x 70 a la A75 en eIA>eg. Otro de los principios es el conocido efecto ocurrido con el mo&imiento relati&o entre un campo magn(tico y un conductor. :-:
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>i es el campo magn(tico el que permanece en reposo y el conductor es el que se mue&e, en (ste aparece una fuer*a electromotri* que no posee energía de por sí, pero que da lugar a corrientes de igual intensidad y sentido que las orig origin inad adas as si fuer fuera a el camp campo o magn magn(t (tic ico o el mó&il. $or el contrario, si fuera el conductor el que permanece fio y es el campo magn(tico el que se mue&e, en el entorno del campo magn(tico aparece un campo el(ctrico que posee cierta energía que origina una corriente en los lugares del conductor expuesto al campo magn(tico. Es importante mencionar que la fuer*a magn(tica es 7000 a 70G0 &eces mayor que la fuer*a gra&itatoria. :?:
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En Costa 8ica, en la u#icación 6eográfica de coordenadas )atitud F 21 55J 7KJJ )ongitud F KG1 4J 7/JJ O El Dluo Magn(tico terrestre &ertical medido con un magnetómetro T=$6' M> : 98 B=>594 magnetic >ensor manufacturado por =amaha Corp, en este sitio, se encontró que el fluo magn(tico @ corresponde a 9 x 70 a la A5 ;e#er< metro cuadrado. Con Con este este flu fluo o magn magn(t (tic ico, o, la capa capaci cida dad d de inducción el(ctrica por espira de una #o#ina de un área de un metro cuadrado, sería de 0.773 x 70 : 4 Iolt.< Espira. $ara lograr la diferencia de potencial que se requiera alcan*ar, esto se reduce a un simple pro#lema de diseLo, área de la #o#ina y del n-mero de espiras de la misma. : &* :
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' ! DE(INICION DE "NIDADES
En esta esta capí capítu tullo se prese resent ntan an de maner anera a escueta y muy resumidamente las principales unidades utili*adas en este tra#ao, las cuales se reto retoma mará rán n en las cons consid ider erac acio ione ness para para o#tener los resultados mostrados en el capitulo umero Cinco donde se expone la metodología empleada para o#tener la generación el(ctrica con el uso del campo magn(tico terrestre. $rincipales nidades' - Constante de Planck
)a constante de $lanc% !h" es la relación entre la cantidad de energía y de frecuencia !f" de la onda asociada a un cuantum o a una partícula elemental. Esto se representa por la ecuación E F h.f : && <
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?onde E corresponde a energia, h la constante de $lanc% y f la frecuencia en ciclos por segundo. El Ialor Ialor de h corresponde a h F 3.3437 x 70 a la :9G ulios . >eg. y tam#i(n el &alor de h, hF G.795/ x 70 a la A75 eI . >eg.
Esto
conforme el sistema de unidades de medida utili*ado. )a radiación electromagn(tica se transmite en cantidades discretas, definidas y no contínuas y esta estass cant cantid idad ades es son son m-lt m-ltip iplo loss de n-me n-meros ros enteros. Estas radiaciones se pueden modelar como como osci oscila lado dore ress sinc sincrN rNni nico coss con con ener energi gia a cuántica. - J!"#
Tra# Tra#a ao o nece necesar sario io para para mo&e mo&err una una carg carga a
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- $!$C%' (#!%"# (#!%"# ) e( *
eI es la Energía de mo&er un electrón cuando la diferencia de potencial en un &oltio. n eI F 7.3047/3 x 70 a la A72 Hulios. A ;E@E8 El Dlu Dluo o Magn( Magn(titico co esta esta repres represen enta tado do por líneas de fuer*a magn(tica. )a nidad de fluo fluo magn(tico en una sola línea de fuer*a, design designada ada Max+ Max+ell ell.. El n-mero n-mero de línea líneass de fuer*a que pasan perpendicularmente por un centímetro cuadrado se llama densidad de fluo y se mide en 6auss. n 6auss F a un Max+ell Max+ell < Cm. cuadrado. )a nidad de fluo magn(tico en el sistema M> en el ;e#er < metro cuadrado, el cual equi&ale a 70,000 gauss.
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6auss' n 6auss se define como un Max+ell por cent centím ímet etro ro cuadr cuadrad ado. o.
Es la inte intens nsid idad ad de
campo que o#ra con una fuer*a de una ?ina, so#re un polo cuya intensidad magn(tica es de una unidad C6>. Max+ell' n Max+ell se define como el fluo magn(tico total alrededor de la superficie, en un área de un cent centím ímet etro ro cuad cuadra rado do,, perp perpen endi dicu cula larr al campo magn(tico. 7 Max+ell F 7 6auss F a 70 a la AK ;e#er, ;e#er, Colum#io' n Colum#io es la cantidad de carga el(ctrica
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de un amperio de intensidad. 7 Colum#io F 7 mperio . >egundo 7 Colum#io F 7 D . I Carga el(ctrica de un Electrón B En Ioltios Ioltios ' Carga del Electrón Electrón F 0.73 x 70 a la :74 Ioltios. Ioltios. Daradio' n faradio es la capacidad de un condensador entre cuyas armaduras existe una diferencia de pote potenc ncia iall el(ct el(ctri rico co de un &olt &oltio io cuan cuando do esta esta cargado de una cantidad de electricidad igual a un colum#io.
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G ! CAMPO MAGNETICO TERRESTRE El campo magn(tico terrestre es #astante d(#il, es del orden de 0,9 gauss en las proximidades del ecuador y de 0,/ gauss en las regiones polares, sin em#argo es 7000 a 70G0 &eces mas fuerte que el campo gra&itatorio. )a existencia del campo magn(tico terrestre es conocido desde la antigPedad por su aplicación en la na&egación a tra&(s de la #r-ula. El físico ingl(s, ;illiam 6il#ert, talló un imán en forma esf(rica y estudió en (l la distri#ución del campo magn(tico en su superficie encontrando que todo coincidía con lo que se
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representación real de este campo sería el de un imán esf(rico cuyo ee de rotación estu&iera des&iado unos 701 del ee geográfico de la Tierra. >i se toma un imán y se suspende hori*ontalmente con li#re rotación,
este
adopta una posición tal que uno de sus extremos apunta aproximadamente hacia el polo norte geográfico. este extremo se le llama llama polo norte del imánQ al extremo opuesto
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por lo tanto la #r-ula indica cuál es la dirección de la línea geográfica geográfica orteA>ur sólo de un modo aproximado, es decir los dos puntos donde el ee de rotación de la Tierra corta a la superficie terrestre. Ier Digura o. 7. ormalmente, la agua de la #r-ula #r-ula se des&ía hacia el Este o hacia el Oeste del norte geográfico. Este ángulo ángulo de des&iación se denomina declinación.
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: &- <
la hori*ontal se llama inclinación magn(tica.
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la superficie de la Tierra. Tierra. El alineamiento en general orteA>ur de las líneas magn(ticas, de acuerdo con el ee de rotación terrestre, sugiere que el campo, en lo fundamentalQ constituye un dipolo. 8esulta inclinado unos 701 respecto al ee de rotación terrestre,
y
presenta
considera#les
irregularidades. El origen de la existencia del campo magn(tico terrestre se ha tratado de explicar con diferentes teorías las que en su totalidad se
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)os estudios geofísicos muestran la existencia de un n-cleo terrestre de naturale*a fluida y alta densidad, compuesto casi en su totalidad de hierro, estos estudios sir&en de #ase a las teorías que sit-an el origen del campo magn(tico en procesos dinámicos que tienen lugar en su interior. El fenómeno se #asa en que el mo&imiento de circulación de material conductor en presencia de
un
campo
magn(tico genera corrientes el(ctricas que, a su &e*, realimentan el campo inductor. En la
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el campo magn(tico terrestre no es constante, sino que cam#ia continuamente. Ray una &ariación pequeLa y #astante regular de un día a otro B&ariación diurna. )a &ariación en la declinación es de algunos minutos de arco, y la &ariación en la la intensidad intensidad es del orden de 70 a la AG gauss.
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sólo se aprecian al comparar &alores medios anuales durante &arios aLos, reci#en el nom#re de &ariación secular. n fenómeno
de la
&ariación secular hace referencia a que la distri#ución del campo geomagn(tico se mue&e lentamente hacia el Oeste. El promedio de a&ance es de muy #aa &elocidad por aLo, con
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En &irtud de que la &ariación secular es tan lenta que requiere de 4,000 aLos para dar una &uelta completa alrededor el ee de rotación, y las anomalías a largo pla*o no se toman en cuenta por su duración de millones de aLos, por lo que cualquier in&ersión en el $royecto de 6ene 6enera raci ción ón El(ct l(ctri rica ca uti utili*a li*and ndo o el cam campo
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+ ! CONSIDERACIONES CONSIDERAC IONES PARA PARA GENERACI,N GENERACI, N ELECTRICA CON EL CAMPO MAGNETICO TERRESTRE
En
el
desarrollo
de
este
capítulo
se
menc mencio iona nará rán n los los princ princip ipal ales es conce concept ptos os que que pri priman para ara cons consid ide erar rar la posi posi#i #ililida dad d de generar
electricidad
apro&echando
las
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El(ctrica utili*ando el campo geomagn(tico , se parte parte de consid considera erarr que el n-mero n-mero de línea líneass de fuer*a de un campo magn(tico por metro cuadrado y por segundo es igual al n-mero de cuantum de acción B h por metro cuadrado y por por segu segund ndo, o, esta esta#l #lec eci( i(nd ndos ose e la sigu siguie ient nte e ecuación.
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@ F ?ensidad del Dluo Magn(tico.
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: )> <
cial en &oltios &oltios , sería'
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: )- <
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se reali*ó nue&amente otra lectura, solamente que en esta ocasión se utili*aron las escalas de
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magn(tico terrestre y las características propias
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