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A fixed horizontal wire carries a current of 200 A. Another wire having a mass per unit length $10^{- 2} kg / m$ is placed below the first wire at a distance of 2 cm and parallel to it. How much current must be passed through the second wire if it floats in air without any support? What should be the direction of current in it

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49 A (direction of current is opposite to first wire)

49 A (direction of current is same as first wire)

25 A (direction of current is same as first wire)

25 A (direction of current is opposite to first wire)

answer is C.

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Detailed Solution

For floating the second wire

weight of second wire = Magnetic force on it

$\Rightarrow F_{B} = m g$

$\Rightarrow m g = \frac{μ_{0}}{4 π} \cdot \frac{2 i_{1} i_{2}}{a} \times l$

$\Rightarrow (\frac{m}{l}) g = \frac{μ_{0}}{4 π} \cdot \frac{2 i_{1} i_{2}}{a}$
$\Rightarrow 10^{- 2} \times 9.8 = 10^{- 7} \times \frac{2 \times 200 \times i}{2 \times 10^{- 2}}$

$\Rightarrow i = 49 A$

(Direction of current is same as first wire, so that attraction force will act between them)

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