Physics

The key insight is that magnetic flux measures how many field lines pierce through a surface—it depends on the component of the field perpendicular to the loop's plane. When the loop's plane is parallel to the field lines, the field runs along the surface rather than through it, so no field lines actually pass through the enclosed area. Mathematically, $\Phi = BA\cos\theta$, and when the plane is parallel to $\vec{B}$, the angle between the field and the normal to the loop becomes 90°, making $\cos(90°) = 0$.

The key insight is that magnetic flux measures how many field lines pierce through a surface—it depends on the component of the field perpendicular to the loop's plane. When the loop's plane is parallel to the field lines, the field runs along the surface rather than through it, so no field lines actually pass through the enclosed area. Mathematically, $\Phi = BA\cos\theta$, and when the plane is parallel to $\vec{B}$, the angle between the field and the normal to the loop becomes 90°, making $\cos(90°) = 0$.