Question

Two long parallel wires carrying currents $8 A$ and $15 A$ in opposite directions are placed at a distance of $7 cm$ from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of magnetic field at $P$ is ___$\times 10^{-6} T$ (Given : $\sqrt{2}=1-4$ )

Answer 1

Magnetic fields due to both wires will be perpendicular to each other.
$B_1=\frac{\mu_0 i_1}{2 \pi d } B_2=\frac{\mu_0 i _2}{2 \pi d } $
$ B _{ net }=\sqrt{ B _1^2+ B _2^2} \Rightarrow \frac{\mu_0}{2 \pi d } \sqrt{ i _1^2+ i _2^2} $
$\Rightarrow \frac{4 \pi \times 10^{-7}}{2 \pi \times(7 / \sqrt{2}) \times 10^{-2}} \times \sqrt{8^2+15^2}\left( d =\frac{7}{\sqrt{2}} cm \right)$
$ \Rightarrow 68 \times 10^{-6} T$