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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.

A thin, metallic spherical shell of radius 0.297 m has a total charge of 5.03 × 10⁻⁶ C placed on it. A point charge of 4.65 × 10⁻⁶ C is placed at the center of the shell. What is the electric field magnitude E a distance 0.795 m from the center of the spherical shell? Does the electric field point outward from the center of the sphere or inward?

This problem explores the electric field produced by a thin metallic spherical shell with a total charge of 5.03 × 10⁻⁶ C, and a point charge of 4.65 × 10⁻⁶ C placed at the center. Learn how to calculate the electric field at a distance of 0.795 m from the center using principles of electrostatics and Gauss's law.

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