Question

Two long parallel wires carrying currents $8A$ and $15A$ in opposite directions are placed at a distance of $7cm$ 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

Answer: 68

Magnetic fields due to both wires will be perpendicular to each other.
$B_1=\frac{{\mu }_0{i}_1}{2\pi d}{B}_2=\frac{{\mu }_0{i}_2}{2\pi d}$
$B_{net}=\sqrt{B_1^2+B_2^2}\Rightarrow \frac{{\mu }_0}{2\pi d}\sqrt{i_1^2+i_2^2}$
$\Rightarrow \frac{4\pi \times 10^{-7}}{2\pi \times (7/\sqrt{2})\times 10^{-2}}\times \sqrt{8^2+15^2}\left(d=\frac{7}{\sqrt{2}}cm\right)$
$\Rightarrow 68\times 10^{-6}T$