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Two infinitely long parallel conducting wires A and B carry currents I and 2I, respectively, in the same direction. The wire A has uniform mass per unit length $\lambda$ and lies on an insulated floor. The wire B is kept fixed at a height h above the floor. The minimum magnitude of h so that the wire A does not rise from the floor is: [g is the acceleration due to gravity and $\mu_0$ is the permeability of free space.]
Detailed Solution
Wire A does not rise when the magnetic attraction per unit length just equals its weight per unit length: $\frac{F_m}{l}=\frac{mg}{l}=\lambda g \Rightarrow \frac{\mu_0(2I)(I)}{2\pi h}=\lambda g \Rightarrow h=\frac{\mu_0I^2}{\pi\lambda g}$.
