Final answer:
The magnitude of the electric field E at a distance r outside a charged spherical ball is given by E(r) = (ρ * rb^3) / (3ε0 * r^2), where ρ is the charge density and rb is the radius of the ball.
Step-by-step explanation:
The question is asking for the magnitude of the electric field E at a distance r from the center of a charged spherical ball, assuming the distance is greater than the radius of the ball rb. To find the answer, we can use Gauss's Law. For a spherically symmetric charge distribution, the electric field outside the distribution (r > rb) is as if all the charge were concentrated at the center of the sphere. Therefore, the enclosed charge q can be calculated using the volume charge density ρ (rho) and the volume of the ball with radius rb. The formula for the enclosed charge q is q = ρ * ⅔π * rb^3.
The electric field E(r) at a distance r, where r > rb, can be found using the formula for the electric field due to a point charge: E(r) = (1 / (4πε0)) * (q / r^2), substituting the expression for q we get: E(r) = (ρ * rb^3) / (3ε0 * r^2).