Question

Two straight wires each $10cm$ long are parallel to one another and separated by $2cm$ . When the current flowing in them is $30A$ and $40A$ respectively, the force experienced by either of the wires is

• A. $1.2\times 10^{-3}N$
• B. $12\times 10^{-3}N$
• C. $11.2\times 10^{-3}N$
• D. $10.2\times 10^{-3}N$

Answer 1

Answer: (A)

Force between two parallel wires is
$F=\frac{{\mu }_0}{4\pi }\cdot \frac{2I_1{I}_2}{r}\cdot l$
Given, ${\mu }_0=4\pi \times 10^{-7},I_1=30A,I_2=40A$
$l=10\times 10^{-2}m,r-2\times 10^{-2}m$
$F=\frac{4\pi \times 10^{-7}}{4\pi }\times \frac{2\times 30\times 40}{2\times 10^{-2}}\times \frac{10}{100}$
$\Rightarrow F=1.2\times 10^{-3}N$