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A current carrying wire carries a current of 2A, lies along the z-axis which is out of page, another wire carrying current of 4A in same direction lies parellel to the first. Then around which loop linking both the wires $\int \bar{B} \cdot d \bar{r}$ is zero.

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answer is A.

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Detailed Solution

the left wire is enclosed by two loops and $\oint \vec{B} . d \vec{l} a r o u n d t h e s e t w o l o o p s i s (- 2 μ_{0} - 2 μ_{0}) i . e . - 4 μ_{0} .$

The right wire is enclosed by one loop and along this loop $\oint \vec{B} . d \vec{l} = + 4 μ_{0} .$ Therefore net $\oint \vec{B} . d \vec{l} = 0 .$

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