Solución de Ejercicios de Las Guías de Electromagnetismo

 

\KFRLW^FCOC CL LI ^OIROC@W BON\ISOC M\ISFCF^NFQIFKOWFO CL @NNFCLKSL CLQOWSOMLKS@ CL BF^FNO MOSLWFO8 BF^FNO FFF FKJLKFLWÍO @WFLKSOC@W8 FKJ. FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

J\FO #? ’ ILV CL N@\ N@\I@ I@MG MG V NOM NOMQ@ Q@ LI NSWF NSWFN@ N@” ” 

’Li molstr` mlcf`nrl cfnl, li gulk molstr` lxpifno, li molstr` suplrf`r clmulstro, li jrok molstr` fkspfro” Zfiifom O. Zorc FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

?

 

QW@GILMO^

?.  °Nuïi clgl slr io cfstoknfo lktrl io norjo puktuoi q ? = 72.> ι N y io norjo puktuoi q 7 = - 3:.? ι N n`k `ghlt` cl qul io bulrzo liæntrfno cl otronnfþk lktrl liios tlkjo uko mojkftuc cl x?1-2 N

r=0



Nïinui` cl ios mojkftucls8

 

 

 

^ljøk li cfojromo cl bulrzos sl tflkl8

o)   g) 

 

 

FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

>

 

>.  C`s norjos p`sftfvos cl 3.?5 ι N noco uko, y uko norjo kljotfvo cl „  2.>2 ι N, lstïk bfhos lk i`s værtfnls cl uk trfokjui` lqufiïtlr` cl ?>.1 nm cl ioc`. Noinuil io bulrzo liæntrfno s`grl io norjo kljotfvo. q >=-2,>2¼N

?>nm

?>nm

21± ?>nm q ?=3,?5¼N  Jl`mltrío cli pr`gilmo8

q 7=3,?5¼N

Srfïkjui` k`togil cl 21±

∘ ∘  sfk21±= 

 

CNI8 Okïifsfs vlnt`rfoi8

q >  21± 21± Bl?>  Bl7>  Rlnt`rfoimlktl ios n`mp`klktls lk x, sl noknliok 21± Bl?>

Bl?>(sfk21±) 21±

Br Bl7>(sfk21±)

Bl7> Nïinui` cl ios mojkftucls8

6 77 3,3,?5√?122,2,>2√?12  6√?1 B = B = B = ?>√?1∘ ∘ >77 =?3,?2K  =7sfk21±=7?3,?2 2 7  =73,? |?,21 √ ?1?6 N|=?,>7 √ ?1?> ?l-------------------6,?16

 

=5,7>3

k=

 

k------------------:3

2.  Lk io bfjuro m`stroco sl i`noifzok trls norjos puktuoils ugfnocos lk ios lsqufkos cl uk trfokjui` lqufiïtlr`. Noinuil io bulrzo liæntrfno klto s`grl io norjo cl :.1 ι N. y

:.1 ι N 

1.< m

x

7.1 ι N 

- 3.1 ι N

`s21±±  slk21±  n`s21  n`s21± B?

B?

B7

21± 21± B7

B?

 

 

B?

 

B7

BW B7

21±

21±

 

 slk21±

  7√?1  ∗ ∗   7 √?1   :√?1 :√?1  6√?1 ?=? =   1,2n`s ⃚   slk ↗ ? =  7. > 2.      7. > 2.           ∘ ∘  ∘ ∘  ̇ ̇ ⃚   ↗ 7 =    ̇ ̇ ⃚> =   ↗ ⃚> =    Nïinui` cl ios mojkftucls8

 

 

 

 

 7,>2

  31 31  7,<  7,<

 

 

 

 

 

  31 31

 

 

 

 

 

 7,<  7,<

⃚ =  3,:6̇   ̇ ==  3,:6   3131,,2 =31,6  

 31,2

 

 

tok∗ ∗∗,, =5>,7± ↗?51±=72>±

ο=

FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

 

6

 

5.  Lk io bfjuro sl mulstrok trls norjos puktuoils fcæktfnos, noco uko cl moso m = 1.?11 Dj. y cl norjo q, n`ijocos cl trls nulrcos. ^f ios i`kjftucls cl ios nulrcos fzquflrco y clrlneo s`k  I = >1.1 nm y li ïkjui` ε = 311¼N, G (>, 1,7) m N (-?, 7,>) q > 

q 7  G (>, 1,7)

q >=+?11¼N, N (-?, 7,>) m

⃚= ̇ ̇ ⃚ T7717] || =  7 1 7 =7.575 ̇ = |⃚| T ++̇. ̇∗∗] =1.:1:̇1̇1.:1:  O (?, 7,?) - N (-?, 7,>)= (7, 1,-7)

q ?  O (?, 7,?)

 =

 

 

?> ?>

Noinui` cli vlnt`r p`sfnfþk  Mæt`c` cl noglzo mlk`s n` n`io io

 

=

⃚⃚= T33̇7̇] || =  3 7 ? =3. ̇ = |⃚| T∗∗.  +++̇ +] =1.5:>̇1.3>23̇1.7?5  N (-?, 7,>) - G (>, 1,7)= (-3, 7,?)

 =

 

 

7> 7>

=

 

Noinui` cl ios mojkftucls8

  ∗ ∗   7711√?1 ?11√?1 ?>=6√?1 ?>= 6√?1    7 7. 11√?1 . 5 75 75  ? 11√?1   =77. < 1:K    ∗ ∗   6√?1  > >11√?1 11√?1   ?11√?1 ?11√?1    =?7.5= 3.

 

⃚ =77.   ? >1± =  = > >↗ ↗  = >>1±4 >>1±  =  4  =7/> >1  >1± ± = 7    ø    ï       > >/7=7/> /7   ∳

 

 

(?) (7) 

 =3K [ r=7/>E



 =Bl 

Bl=3K

*Io mojkftuc cl ios norjos ls io mfsmo *Io cfstoknfo cl io norjo cl io lsqufko fkblrf`r o io cli nlktr` ls io mfsmo qul io cl io cfstoknfo cl io norjo cli nlktr` o io cl orrfgo

*Q`r i` tokt` io bulrzo liæntrfno ls io mfsmo FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

?5

 

3K +_

3K 3Kn`s>1±

3Kslk>1± >1±

Br 3K

Bl Cl io jrïbfno tlklm`s8

 

 

 3

⃚⃚ ==  733∘ ∘ >>∘ ∘ ̇̇3 3⃚ =3n`s>1± ̇ ̇ ̇3 slk>1±̇ ⃚ =  7∘ ∘ >>̇7̇ ==  7∘ ∘ >>   77 = 3  

 3

 

 7

 

 

 

 

 

?5.  ^l tflklk trls norjos n`m` sl mulstro lk io bfjuro

,

V 

, Noinuior io bulrzo rlsuitoktl lk _?.

B>? Br Noinui` cl ios mojkftucls8

B7?



>?= 6√?1  ??2√?1 >?=6√?1 2√?1 >>∗∗?√?1 ? √?1∗∗ =311K   6√?1  > >√?1 √?1   ?√?1 ?√?1    7>= =>11K > ⃚ =  ̇>11̇ ==  311   >11>11 = = 777  

q ??== q 77== q >>== q  

 

 

 

 

 = 7 = 7 =?/7

 

71.  Lk io bfjuro sl mulstrok c`s lsblrfiios cl fjuoi tomoÿ` norjocos n`k mojkftuc q y >q

rlsplntfvomlktl. Clsprlnfokc` ios bulrzos cl brfnnfþk, eoiior li pls` cli gi`qul Z, toi qul li sfstlmo  sl lknulktrl lk lqufifgrf`. q = ?1 N

Bl

-q  

Bl

1.>m

+>q  

   ∗    6√?1  > ? ?1√?1 1√?1      > d > >q q  q   =>1K  =  =  = 

 

1.>

FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

 

71

 

S

>1K

Sslk±Sslk S

S ±

Sn`s±

↗ = 1 4   >1 = 14 = = >1 ↟ = 1 4 ±  ±   = 14  = 7±

Sn`s±

 

1 >1 3=35 <

± >d    

7?.  Noinuior li nomp` liæntrfn` lk uko lsqufko cl uk nuocroc` cl 51 nm cl ioc`, sf ios `tros trls lsqufkos sl lknulktrok `nupocos p`r norjos cl ?5.7 x?1 -3 N. +q

+ q  

??>.?nm 51nm Q L7 L?

3

3N   √ ?1  6√?1  ?5. 7   ?=L>=  = 51√ ?17 =7.2√ ?1:K/N   3N  ?5. 7 6√?1 √ ?1    L7=L7 =  = ??>.?√ ?17 =?.75√ ?1:K/N

 

 

FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

7?

 

L?slk3>..?33     7  

 

 

 

 

 

 

FKJ FKC. V MLc. ^OM\LI OC@IB@ C\LßO^ OQOWFNF@

7>

 

73.  Cltlrmfkl li pukt` c`kcl li nomp` liæntrfn` klt` slo nlr`. Rlr bfjuro

?=L7 = ?  ?   =  7.2< ? = =↗?7  =7.3 ?7  7?=1 ?. 3    ¿∘ 3 7¿  7¿   7    = 7 = 7?.3 3?.?.3?  = 7>.7.156….. = ?.57m4  = 7>.7.156….. =1.>6m  

 

 

 

 

 

   

?.57 m o io fzquflrco cl io norjo cl -7.