Final answer:
The magnetic field of a Sun-like star will increase significantly upon collapsing into a neutron star, particularly at the poles due to the conservation of magnetic flux and angular momentum, resulting in particles accelerating to high velocities.
Step-by-step explanation:
When a star like the Sun collapses into a neutron star with a radius of 10km, its magnetic field would undergo significant changes due to the conservation of magnetic flux. The magnetic field strength would be much higher due to the star's much smaller diameter compared to its original size. In physics, we use the conservation principles to understand these changes. The original magnetic field of the Sun, for instance, would be highly compressed upon collapsing to neutron star dimensions. Due to the conservation of angular momentum, even a slowly rotating star would end up spinning rapidly as a neutron star, with a rotation period of just a fraction of a second. This rapid rotation further strengthens the magnetic field and affects its distribution.
The augmentation of the magnetic field would cause trapped particles such as protons and electrons to accelerate nearly to the speed of light in the outer layers of the neutron star. The behavior of these particles is similar to what we see with charged particles interacting with the Earth's magnetic field, resulting in phenomena like auroras at the poles. Therefore, after such a collapse, the surface magnetic field at the poles of the neutron star can be expected to be extremely intense and much higher than that of the original Sun.