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Question

An otherwise infinite, straight wire has two concentric loops of radii $$a$$ and $$b$$ carrying equal currents in opposite directions as shown in figure. The magnetic field at the common center is zero for:

166818.PNG


A
ab=π1π
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B
ab=ππ+1
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C
ab=π1π+1
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D
ab=π+1π1
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Solution

The correct option is B $$\cfrac { a }{ b } =\cfrac { \pi } { \pi +1 }$$
$${ B }_{ centre }=0$$
$$\cfrac { { \mu  }_{ 0 }I }{ 4\pi b } \bigodot +\cfrac { { \mu  }_{ 0 }I }{ 4\pi b } \bigodot +\cfrac { { \mu  }_{ 0 }I }{ 2b } \bigodot +\cfrac { { \mu  }_{ 0 }I }{ 2a } \bigotimes =0$$
$$\Rightarrow \cfrac { { \mu  }_{ 0 }I }{ 2\pi b } +\cfrac { { \mu  }_{ 0 }I }{ 2b } -\cfrac { { \mu  }_{ 0 }I }{ 2a } \Rightarrow \cfrac { 1 }{ 2\pi b } +\cfrac { 1 }{ 2b } =\cfrac { 1 }{ 2a } $$
$$\Rightarrow \cfrac { a }{ b } =\cfrac { \pi  }{ \pi +1 } $$

Physics
NCERT
Standard XII

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