Question

Two parallel, long wires are kept $0.20m$ apart in vacuum, each carrying current of $xA$ in the same direction. If the force of attraction per meter of each wire is $2\times 10^{-6}N$, then the value of $x$ is approximately:

• A. 1
• B. 2.4
• C. 1.4
• D. 2

Answer 1

Answer: (C)

Force per unit length $=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$
$=\frac{{\mu }_0\cdot x^2}{2\pi \times 0.2}$
$F=2\times 10^{-6}=\frac{4\pi \times 10^{-7}\times x^2}{2\pi \times 0.2}$
$\Rightarrow 10^{-6}=10^{-7}\frac{x^2}{0.2}$
$\Rightarrow x^2=10\times 0.2$
$=2$
$\Rightarrow x=\sqrt{2}\approx 1.4Amp$