Radial density

Definition

Radial density is a function that describes how mass or charge is distributed as a function of distance from a central point. It is often used in physical applications involving symmetry.

5 Must Know Facts For Your Next Test

1. Radial density functions are commonly integrated over spherical coordinates to find total mass or charge.
2. The radial density function, denoted as $\rho(r)$, depends on the radial distance $r$ from the origin.
3. In spherical coordinates, volume elements are given by $dV = r^2 \sin(\theta) dr d\theta d\phi$.
4. When integrating radial density over a sphere, the integral limits for $r$ range from 0 to the radius of the sphere.
5. Radial density can be used to solve problems involving gravitational fields and electrostatics.

Review Questions

Related terms

Volume Element: A differential element used in integration to calculate volumes; in spherical coordinates, it is expressed as $dV = r^2 \sin(\theta) dr d\theta d\phi$.

Spherical Coordinates: A coordinate system where points are defined by their distance from the origin (radius), angle from the positive z-axis (polar angle), and angle from the positive x-axis in the xy-plane (azimuthal angle).

Gravitational Field: A vector field that represents the gravitational force per unit mass at each point in space.