A wire $AB$ is carrying a steady current of $12 A$ and is lying on the table. Another wire $CD$ carrying $5A$ is held directly above $AB$ 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 $g = 10 ms^{–2}]$
CBSE OUTSIDE DELHI - SET 1 2013
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Concepts:
$1.$ Current carrying conductors repel each other, if current flows in the opposite direction.
$2.$ Attract each other if current flows in the same direction.
If wire $CD$ remain suspended above $AB$ then
$F_{repulsion} =$Weight
$\frac{\mu_{0}\text{I}_{1}\text{I}_{2}l}{2\pi\text{r}} = \text{mg}$
where $r =$ Separation between the wires
$\frac{\text{m}}{l} = \frac{\mu_{0}\text{I}_{1}\text{I}_{2}}{2\pi\text{rg}}$
$ = \frac{2\times10^{-7}\times12\times5}{1\times10^{-3}\times10}$
$=1.2\times10^{–3} \text{kg/m}$
Current in $CD$ should be in opposite direction to that in $AB.$
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