A wire AB is carrying a steady currents of 12 A and is lying on a table. Another wire CD carrying 5A is held directly above BA at a height of 1 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of `g=10 m*s^(-2)]`

Explanation

We take unit length of each of the wires.
Upward force on CD,
`F=(mu_(0))/(4pi)(2I_(1)I_(2))/(d)=10^(-7)xx(2xx12xx5)/(10^(-3))=12xx10^(-3)N`
Downward force on CD,
`F'mg=10mN`
[ m=mass of unit length of the wire CD]
Under the given condition,
`F=F' or, 12xx10^(-3)=10 m`
or `m=1.2xx10^(-3)=10m`
The currents in AB and CD are in opposite directions, so that CD is subjected to an upward repulsive force F.