Question

Two long parallel wires carrying equal current separated by $1m$ exert a force $2\times {10}^{-7}N/m$ on one another. The current flowing through them is

• A. $2.0A$
• B. $2.0\times {10}^{-7}A$
• C. $1.0A$
• D. $1.0\times {10}^{-7}A$

Answer 1

The correct option is C $1.0A$

$\frac{F}{l}=\frac{{\mu }_0}{4\pi }\times \frac{2i_1{i}_2}{a}$

$\Rightarrow \frac{F}{l}=\frac{{\mu }_0}{4\pi }\frac{2i^2}{a}(\because i_1=i_2=i)$
$\Rightarrow 2\times {10}^{-7}={10}^{-7}\times \frac{2i^2}{1}$

$\Rightarrow i=1A$