Final answer:
The greatest density of magnetic flux lines in a rotating magnet-type magneto occurs at the position where the magnetic flux reaches its maximum. This happens when the magnet's poles are perpendicular to the coil, leading to a maximum density of magnetic flux lines and the strongest magnetic field.
Step-by-step explanation:
The greatest density of flux lines in the magnetic circuit of a rotating magnet-type magneto occurs when the magnet is in the position where the magnetic flux is at a maximum. The density of the magnetic field is directly related to the number of magnetic flux lines per unit area. When the magnet is aligned such that its poles are perpendicular to the coil, the area vector of the coil and the magnetic field vector are either parallel or anti-parallel, resulting in the maximum magnetic flux. At this position, the magnetic flux lines are most densely packed, and thus the magnetic field is strongest. Considering the torque experienced by a magnetic compass needle, it will be greatest when the density of the magnetic field is at its maximum. Additionally, it's important to note that the emf induced in a coil rotating within a magnetic field is maximum when the change in magnetic flux is at its maximum, which occurs when the magnetic flux changes from its maximum to zero, as seen during a quarter revolution of the coil in a generator.