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Two thin long straight wires are arranged parallel to each other with a separation of 1 m. Current in one of the wires is 2A. Null point is found to be at a distance 2m from it and 3m from the other conductor in the plane of the conductors, but outside the conductors. The force exerted by each conductor per unit length on the other in $N m^{- 1}$ is

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$1.2 \times 10^{- 6}, repulsive$

$4 \times 10^{- 6}, replusive$

$4 \times 10^{- 5}, attractive$

$12 \times 10^{- 6}, attractive$

answer is A.

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Detailed Solution

$\frac{I_{2}}{(2 + 1)} = \frac{2}{2} \Rightarrow I_{2} = 3 A$ in opposite direction to I₁

$\begin{array}{l} \frac{F}{l} = \frac{μ_{0}}{2 π} \frac{I_{1} I_{2}}{r} = 2 \times 10^{- 7} \times \frac{2 \times 3}{1} \\ = 1.2 \times 10^{- 6} N m^{- 1}, r e p u l s i v e \end{array}$

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