Question

The volume electric charge density of a solid sphere is given by the following equation: The variable r denotes the distance from the center of the sphere, in spherical coordinates. What is the net electric charge (in μC) of the sphere if the radius of the sphere is 0.5 m?

Answer 1

The net electric charge of a solid sphere can be found by integrating the charge density function over the volume of the sphere using spherical coordinates.

Step-by-step explanation:

The volume electric charge density of a solid sphere is given by the equation ρ = ar², where r is the distance from the center of the sphere in spherical coordinates.

To find the net electric charge of the sphere, we need to integrate the charge density function over the volume of the sphere. Since the charge density is given as ρ = ar², we can integrate this function over the volume of the sphere using spherical coordinates.

The volume of a sphere with radius R is given by V = (4/3)πR³. Integrate the charge density function ρ = ar² over the volume of the sphere to get the net electric charge, Q, of the sphere.