A write AB is carrying a steady current of 10A and is lying on the table. Another wire CD carrying 6A is held directly above AB at a height of 2 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 ms^(-2)`]

Explanation

Force per unit length between the current carrying wire is given as :
`" "F=(mu_(0))/(4pi).(2I_(1)I_(2))/(r)`
Where `" "I_(1)="Current in wire"`
`" "AB = 10 A`
`" "I_(2) = "Current in wire"`
`" "CD = 6A`
`r rarr` distance between wires = 2mm = `2 xx 10^(-3)m`
Let m be the mass of wire CD.
As the force balances the weight of the wire
`therefore" "(mu_(0))/(4pi).(2I_(1)I_(2))/(r)=mg rArr 10^(-7) xx (2 xx 10 xx 6)/(2 xx 10^(-3))=m xx 10 rArr m = 10^(-7) xx (2 xx 10 xx 6)/(2 xx 10^(-3))xx(1)/(10) m = 6 xx 10^(-4) kg m^(-1)`.