1. **Problem Statement:** Two long isolated wires are placed perpendicular to each other in the same plane, each carrying a current of intensity $I$. We need to find the points where the resultant magnetic flux density is zero. 2. **Magnetic Field Due to a Long Straight Wire:** The magnetic field $B$ at a distance $r$ from a long straight wire carrying current $I$ is given by: $$ B = \frac{\mu_0 I}{2 \pi r} $$ where $\mu_0$ is the permeability of free space. 3. **Direction of Magnetic Field:** The magnetic field lines form concentric circles around the wire, with direction given by the right-hand rule. 4. **Setup:** The two wires are perpendicular, one along the x-axis and one along the y-axis, intersecting at the origin. Points $a, b, c, d$ are at the corners of a square around the origin. 5. **Resultant Magnetic Field:** At any point, the resultant magnetic field is the vector sum of the fields due to each wire. 6. **Condition for Zero Resultant:** The magnetic fields from the two wires must be equal in magnitude and opposite in direction to cancel out. 7. **Analysis of Points:** - At points $b$ and $d$, the magnetic fields from the two wires have equal magnitude and opposite directions. 8. **Conclusion:** The resultant magnetic flux density vanishes at points $b$ and $d$. **Final answer:** Points $b$ and $d$.