1. The problem involves two parallel wires a and b carrying currents of I and 2I, respectively, with a point y inside the triangle formed by points a, b, and y. 2. The magnetic flux density at point y due to wire a is given as B. 3. Magnetic field due to a long straight current-carrying wire is given by $$B = \frac{\mu_0 I}{2 \pi r}$$ where $r$ is the perpendicular distance from the wire to the point. 4. The wire b carries current 2I; thus, flux density at y due to b is proportional to $2I$ and inversely proportional to its distance from y. 5. Using the geometry, we calculate the resultant flux density magnitude as $$B_{net} = \sqrt{B_a^2 + B_b^2 + 2 B_a B_b \cos \theta}$$ with $\theta$ being the angle between directions of the two fields. 6. Given currents I and 2I, and that fields are perpendicular or at an angle giving resultant $\sqrt{5} B$, the correct choice based on vector addition is $\sqrt{5} B$. Answer: d) $\sqrt{5} B$