• # question_answer                 Two long parallel wires are at a distance of 1 m. Both of them carry one ampere of current. The force of attraction per unit length between the two wires is:                                                                       A)                 $2\times {{10}^{-7}}\,N/m$      B)                 $2\times {{10}^{-8}}\,N/m$      C)                 $5\times {{10}^{-8}}\,N/m$      D)                 ${{10}^{-7}}\,N/m$

Magnetic force between parallel wires per unit length is                 $\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\times \frac{{{i}_{1}}\,\,{{i}_{2}}}{r}$                                 where ${{i}_{1}}$ and ${{i}_{2}}$ are the currents in wires 1 and 2 respectively and r is the distance between them. Since, it is given that between two wires, there is a force of attraction, so the direction of currents in both will be the same.                 Here,                 ${{i}_{1}}={{i}_{2}}=1\,A,\,r=1\,m,$                 ${{\mu }_{0}}=4\pi \times {{10}^{-7}}\,T-m/A$                 $\therefore$  $\frac{F}{l}=\frac{4\pi \times {{10}^{-7}}}{2\pi }\times \frac{1\times 1}{1}$                 $=2\times {{10}^{-7}}\,N/m$