Question

A long horizontal rigidly supported wire carries a current $96\text{A}$. Directly above it and parallel to it at a distance of $3.2\times {10}^{-3}\text{m}$, another wire of weight $0.144\text{N}$ per metre carrying certain current. If the upper wire is to float in air due to magnetic repulsion, then the magnitude and direction of current in the upper wire is.

• A. $12\text{A}$ in the same direction of the lower wire.
• B. $12\text{A}$ in the opposite direction of the lower wire.
• C. $24\text{A}$ in the same direction of the lower wire.
• D. $12\text{A}$ in the opposite direction of the lower wire.

Answer 1

The correct option is D $12\text{A}$ in the opposite direction of the lower wire.

Weight of the wire should be balanced by magnetic force
$W=F$
$W=\frac{{\mu }_0{i}_1{i}_{2}l}{2\pi d}$
$\frac{W}{l}=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$
$0.144=\frac{4\pi \times {10}^{-7}\times 96\times i_2}{2\pi \times 3.2\times {10}^{-3}}$
$i_2=\frac{144}{6}=24\text{A}$
in the opposite direction to the lower wire.