(b) What is the potential difference V(r) - V(0) for r < a (i. e., where r is inside the insulating sphere, and V(0) is the potential at the origin)

it is very well related to a lot of things but with my limited knowledge i can confidently say that the answer is space.

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.