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A very long straight conducting wire, lying along the Z axis carries a current of 2A. The integral $\int \bar{B} \cdot d \bar{l}$ is computed along the straight line PQ where P has the co-ordinates (2cm, 0, 0) and Q has the co-ordinates (2cm, 2cm, 0). The integral has the magnitude (in SI units)

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Zero

$8 π \times 10^{- 7}$

$2 π \times 10^{- 7}$

$π \times 10^{- 7}$

answer is D.

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Detailed Solution

Consider a square of side 4cm centered around the conductor in the xy - plane.

By amper’s law $∮ \bar{B} \cdot d \bar{l} = μ_{0} i$

$\int \bar{B} \cdot d \bar{l}$ for the given line

$= \frac{μ_{0} i}{8} = \frac{4 π \times 10^{- 7} \times 2}{8} = π \times 10^{- 7}$

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