Solução Questão 09 (MNPEF 2015)
Autor: Romeu Nunes de Freitas | Publicado: 2015-11-10T20:05:00-02:00


Questão 09. Dois fios de cobre, retilíneos e
paralelos entre si, conduzindo correntes elétricas com intensidades constantes,
interagem através de forças magnéticas, orientadas de tal forma que os dois
fios se repelem. Sabe‐se
que as intensidades de ambas as forças, sobre a mesma extensão de cada fio, são
iguais. Então:



A)
as correntes elétricas têm a mesma intensidade e mesmo sentido.

B)
não é possível afirmar qual das correntes é a mais intensa, entretanto ambas
possuem o mesmo sentido.

C)
as correntes elétricas têm a mesma intensidade e sentidos diferentes.

D) não é possível afirmar qual
das correntes é a mais intensa, entretanto ambas possuem sentidos diferentes.



SOLUÇÃO:



Da
lei da ação e reação, as intensidades das forças devem ser equivalentes
independentemente das intensidades das correntes.



Quanto
ao sentido, segue a análise vetorial para a força magnética.

Considerando
que os dois fios paralelos estejam orientados na direção vertical, e, com
centros afastados uma distância d. Supondo que o fio 1 da esquerda seja
percorrido por uma corrente i1 com sentido para cima. Da lei de
Ampére, para corrente constante e campo elétrico invariante no tempo a corrente
i1 produz um campo magnético B1 no fio 2.

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         m:val="roman"/>μ<span
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         m:val="roman"/>0<span
      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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         m:val="roman"/>1<span
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O
sentido do campo magnético é convencionado pela regra da mão direita, sendo que
o polegar indica o sentido da corrente e os dedos indicam o sentido do campo.



A
força magnética que surge no fio 2 devido ao campo B1 é:

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       m:val="roman"/>B<span
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       m:val="roman"/>sen<span
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       m:val="roman"/>θ<![endif]--><!--[if !msEquation]-->
 
<!--[endif]-->

Em
que L é o comprimento do fio e θ é o ângulo entre das direções de i2
e B1. Como i2 e B1 são perpendiculares sen θ =
1, logo:

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       m:val="roman"/>F<span
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         m:val="roman"/>μ<span
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         m:val="roman"/>0<span
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         m:val="roman"/>i<span
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         m:val="roman"/>1<span
      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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         m:val="roman"/>i<span
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         m:val="roman"/>2<span
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       m:val="roman"/>2πd<span
  style='font-family:"Cambria Math",serif;mso-fareast-font-family:"Times New Roman";
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     m:val="roman"/>L<![endif]--><!--[if !msEquation]-->
 
<!--[endif]-->

A
direção da força F2 é convencionada pela regra da mão direita: o
polegar indica a força F2, o indicador indica a corrente i2
e o dedo médio indica o campo B1. Para que ocorra repulsão entre os
fios, a força F2 deve ter sentido para a direita. Da direção do
campo B1 no fio 2, conclui-se que a corrente i2 deve ter
sentido para baixo.




Portanto
as correntes possuem sentidos contrários, porém nada se pode afirmar com
relação às intensidades.