Let's solve the problem step by step.

Given:

• Radius of the spherical shell, $r = 0.297 \, \text{m}$
• Charge on the spherical shell, $Q = 5.03 \times 10^{-6} \, \text{C}$
• Point charge at the center, $q = 4.65 \times 10^{-6} \, \text{C}$
• Distance from the center where we need to find the electric field, $r' = 0.795 \, \text{m}$

Step 1: Electric field outside the spherical shell

For a spherical shell, the electric field outside behaves as if the total charge were concentrated at the center. Therefore, to calculate the electric field at a point outside the shell, we can use the formula for the electric field due to a point charge:

$E = \frac{1}{4 \pi \epsilon_0} \frac{Q_{\text{total}}}{r'^2}$

where:

• $Q_{\text{total}} = Q + q$ is the total charge
• $r'$ is the distance from the center
• $\epsilon_0 = 8.854 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2$ is the permittivity of free space

Step 2: Calculating $Q_{\text{total}}$

$Q_{\text{total}} = 5.03 \times 10^{-6} \, \text{C} + 4.65 \times 10^{-6} \, \text{C} = 9.68 \times 10^{-6} \, \text{C}$

Step 3: Substituting into the electric field equation

We substitute the total charge and distance into the formula:

$E = \frac{1}{4 \pi \times 8.854 \times 10^{-12}} \frac{9.68 \times 10^{-6}}{(0.795)^2}$

I'll compute this now.