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A very long, straight conducting wire, lying along the z-axis carries a current of 2A. The integral $\int \vec{B} \cdot \vec{d l}$ is computed along the straight line PQ, where P has the coordinates (2 cm, $0$ , $0$ ) and Q has the coordinates $(2 c m, 2 c m, 0) .$ The integral has the magnitude (in SI units) is $\frac{π}{x} \times 10^{- y}$ then the value of $x + y$ is ___________.

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Detailed Solution

$\int_{P A Q} \vec{B} \cdot \vec{d l} = \int_{R P Q} \vec{B} \cdot \vec{d l} = \frac{μ_{0} I}{2 π R} (\frac{π}{4} R) = (4 π \times \frac{10^{- 7}}{8}) \times 2 = π \times 10^{- 7} T$

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Given is $\frac{π}{x} \times 10^{- y}$

$∴ x = 1 & y = 7$

$x + y = 1 + 7 = 8$

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