It seems you've uploaded a physics problem involving electrostatics. The task is to calculate the electric field and energy related to a uniformly distributed charge within a sphere. Let's break down the problem:

Given:

• Charge $Q = 8 \times 10^{-6} \, C$
• Radius of the sphere $R = 18 \, \text{cm} = 0.18 \, \text{m}$
• The permittivity of free space $\varepsilon_0 = 8.85 \times 10^{-12} \, \frac{\text{C}^2}{\text{N} \, \text{m}^2}$

The problem asks for:

1. The distance from the center to point $P_1$ (inside the sphere).
2. The distance from the center to point $P_2$ (outside the sphere).
3. The electrostatic energy of the charge distribution.

To calculate the distance of $P_1$ and $P_2$, we use the following principles:

• Electric Field Inside the Sphere ($P_1$): For a uniformly charged sphere, the electric field inside the sphere increases linearly with distance from the center. $E_{\text{inside}} = \frac{Q}{4 \pi \varepsilon_0 R^3} r$ where $r$ is the distance from the center to point $P_1$.

• Electric Field Outside the Sphere ($P_2$): For points outside the sphere, the electric field behaves as if all the charge were concentrated at the center. $E_{\text{outside}} = \frac{Q}{4 \pi \varepsilon_0 r^2}$ where $r$ is the distance from the center to point $P_2$.

To calculate the electrostatic energy $U$, we use: $U = \frac{3}{5} \cdot \frac{Q^2}{4 \pi \varepsilon_0 R}$

Now, would you like to proceed with the calculations for these? If you need further clarification on any part, feel free to ask!