**Part A**

The magnitude of the electric field can be calculated from the center of the ball.

According to Gauss's law:

$\mathbf{\int}\mathit{E}\mathbf{\xb7}\mathit{d}\mathit{A}\mathbf{=}\frac{\mathbf{q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}$

Let's consider the ball to be a sphere.

A solid ball of radius r_{b} has a uniform charge density ρ.**Part A**

What is the magnitude of the electric field E(r) at a distance r > r_{b} from the center of the ball? Express your answer in terms of ρ, r_{b}, r, and ϵ_{0}.

**Part B**

What is the magnitude of the electric field *E*(*r*) at a distance *r *< *r** _{b}* from the center of the ball?

Express your answer in terms of *ρ*, *r*, *r*_{b}, and *ϵ*_{0}.

**Part C.**

Let E(r) represent the electric field due to the charged ball throughout all of space. Which of the following statements about the electric field are true?

1. E(0) = 0

2. E(r_{b}) = 0.

3.

4. The maximum electric field occurs when r = 0.

5. The maximum electric field occurs when r = r_{b}.

6. The maximum electric field occurs as r → ∞.

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