Q. 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
A) 25 A (direction of current is same to first wire)
B) 25 A (direction of current is opposite to first wire)
C) 49 A (direction of current is same to first wire)
D) 49 A (direction of current is opposite to first wire)
Explanation
(c) For floating the second wire
$\left| \begin{matrix}
Downward\ weight \\
of\ second\ wire
\end{matrix} \right| = \left| \begin{matrix}
Magnetic\ force \\
on\ it
\end{matrix} \right|$
$\Rightarrow mg = \frac{\mu_{0}}{4\pi}.\frac{2i_{1}i_{2}}{a} \times l$
$\Rightarrow \left( \frac{m}{l} \right)g = \frac{\mu_{0}}{4\pi}.\frac{2i_{1}i_{2}}{a}$
$\Rightarrow 10^{- 2} \times 9.8 = 10^{- 7} \times \frac{2 \times 200 \times i}{2 \times 10^{- 2}} \Rightarrow i = 49A$
(Direction of current is same to first wire)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.