Two long parallel wires carrying currents $8\ \text{A}$ and $15\ \text{A}$ in opposite directions are placed at a distance of $7\ \text{cm}$ 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 ______ $\times10^{-6}\ \text{T}$. (Given $\sqrt2=1.4$)
Numerical value type. Enter your answer.
Answer: 68
$P$ is at distance $r=\dfrac{7}{\sqrt2}=5\ \text{cm}$ from each wire. The two fields are perpendicular to the lines joining $P$ to the wires, so they are perpendicular to each other:
$$B=\frac{\mu_0}{2\pi r}\sqrt{8^2+15^2}=\frac{2\times10^{-7}}{0.05}\times17=68\times10^{-6}\ \text{T}$$
Solution by Sreeraj P, M.Sc Physics