Question

Two parallel, long wires are kept $0.20\, m$ apart in vacuum, each carrying current of $x\, A$ 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 $
$\Rightarrow x =\sqrt{2} \approx 1.4\, Amp$