Two infinitely long parallel conductors A and B , separated by $\displaystyle 2$ cm , carry $\displaystyle 6$ A and $\displaystyle 2$ A currents in opposite directions respectively. Find :

(a)

the net magnetic field at a point midway between A and B .

(b)

the force acting per unit length on $\displaystyle \mathrm{B}$.

$\displaystyle 1$ \[\text { (a) } \begin{aligned} \mathrm{B}_{1} & =\frac{\mu_{0} I_{1}}{2 \pi r}=\frac{2 \times 10^{-7} \times 6}{1 \times 10^{-2}} \\ & =1.2 \times 10^{-4} \mathrm{~T} \quad \text { into the page } \end{aligned} \] \[\begin{aligned} \mathrm{B}_{2} & =\frac{\mu_{0} I_{2}}{2 \pi r}=\frac{2 \times 10^{-7} \times 2}{1 \times 10^{-2}} \\ & =0.4 \times 10^{-4} \mathrm{~T} \quad \text { into the page } \end{aligned} \] \(\displaystyle \because \mathrm{B}_{1}\) and \(\displaystyle \mathrm{B}_{2}\) are in same direction. \[\begin{aligned} \mathrm{B}_{n e t} & =\mathrm{B}_{1}+\mathrm{B}_{2} \\ & =1.2 \times 10^{-4} \mathrm{~T}+0.4 \times 10^{-4} \mathrm{~T} \end{aligned} \]