Two parallel conducting wires of equal length are placed distance $d$ apart carry current $I_1$ and $I_2$…
Two parallel conducting wires of equal length are placed distance $d$ apart carry current $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is
$\frac{\mu_0\left(I_1-I_2\right)}{2 \pi d}$
$\frac{\mu_0\left(I_1+I_2\right)}{2 \pi d}$
$\frac{\mu_0\left(I_1+I_2\right)}{\pi d}$
$\frac{\mu_0\left(I_1-I_2\right)}{\pi d}$
Solution
Field due to a current-carrying long wire is given by
$B=\frac{\mu_0 I}{2 \pi r}$
The field at the midpoint between the two wires are in the same direction and hence get added.
The distance of the midpoint $r=\frac{d}{2}$
$\begin{aligned} & \therefore B=B_1+B_2=\frac{\mu_0 I_1}{2 \pi\left(\frac{d}{2}\right)}+\frac{\mu_0 I_2}{2 \pi\left(\frac{d}{2}\right)} \\ & =\frac{\mu_0\left(I_1+I_2\right)}{2 \pi\left(\frac{d}{2}\right)}\end{aligned}$
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