Question

Wrrite an expression for the volume charge density rho of a solid sphere

A) rho = Q / V, where Q represents the total charge and V is the volume of the solid sphere.
B) rho = Q / (4/3 * π * r³), where Q is the total charge and r is the radius of the solid sphere.
C) rho = Q / (2 * π * r), where Q stands for the total charge and r represents the radius of the solid sphere.
D) rho = Q / (π * r²), where Q is the total charge and r is the radius of the solid sphere.

Answer 1

The correct expression for the volume charge density of a solid sphere is ρ = Q / (4/3 * π * r³), where Q is the total charge and r is the radius of the solid sphere.

Step-by-step explanation:

The correct expression for the volume charge density ρ of a solid sphere is option B) ρ = Q / (4/3 * π * r³), where Q is the total charge and r is the radius of the solid sphere.

The volume of a sphere is given by V = 4/3 * π * r³. Since the charge density is defined as the ratio of the charge to the volume, we have ρ = Q / V. Substituting the expression for the volume of a sphere, we get ρ = Q / (4/3 * π * r³).