Question

The given figure shows infinitely long bent wires in the $x-y$ plane of paper and each carrying a current $i$. Here $O$ is the origin. Co-ordinates of points $P$ and $Q$ are $(2m,0)$ and $(6m,0)$, respectively. Magnetic induction at $P$ is given by $\frac{\alpha {\mu }_{0}i}{32\pi }$. Find the value of $\alpha$.

Answer 1

Answer: 6

Magnetic field at $P$ is only due to portion $AO$ and $BQ$ and direction of field at $P$ due to both section will be same.
$\therefore B_P=\frac{{\mu }_{0}i}{4\pi \times 2}+\frac{{\mu }_{0}i}{4\pi \times 4}=\frac{3{\mu }_{0}i}{16\pi }$