Discussion Questions Solutions | Physics Galaxy

: As (d \to R^+), (F \to -\infty) (image charge (q') increases and distance to image decreases). The force becomes very strong — but before touching, the point charge induces large surface charge density, leading to possible discharge or breakdown. If the sphere is grounded, then image charge (q' = -\fracRd q) still holds but total charge on sphere is not zero.

| Discussion Topic | Core Physics Concept | Mathematical Takeaway | |----------------|----------------------|------------------------| | Rotation curves | Dark matter halo density profile | (\rho(r) \propto r^-2) → (v(r) = \textconst) | | Spiral arms | Density waves & pattern speed | (\Omega_p \neq \Omega(r)); wave dispersion relation | | AGN energy | Gravitational accretion efficiency | (\eta \sim 0.05-0.4), (L \leq L_\textEdd) | | Hubble expansion | Metric expansion of space | (v = H_0 d) from (ds^2 = -c^2 dt^2 + a(t)^2 d\Sigma^2) | physics galaxy discussion questions solutions

Static friction is generally greater than kinetic friction. For example, it is harder to start moving a heavy box than to keep it moving, due to the difference between static and kinetic friction. : As (d \to R^+), (F \to -\infty)

Prepare students for the "Advanced Illustrations" and "Brain Openers" found in later sections of the books. Solution Methodologies | Discussion Topic | Core Physics Concept |