To determine the electric field at the center of a hollow metal sphere, we can apply Gauss's Law from electrostatics. According to Gauss's Law, the electric field inside a conductor in electrostatic equilibrium is zero. This holds for any point inside the hollow region of the sphere, including the center, regardless of the charges on the surface.

Explanation:

1. The excess electrons are distributed uniformly on the outer surface of the hollow metal sphere.
2. Inside the sphere (including the center), there is no net electric field because, by symmetry, the electric field contributions from all parts of the charged surface cancel each other out.

Final Answer:

The electric field at the center of the hollow metal sphere is: $\mathbf{E}_{\text{center}} = 0 \, \text{N/C}$

Would you like further details on how Gauss's Law applies in this scenario, or do you have any additional questions?

Here are 5 questions you might be interested in:

1. What is the electric field outside the hollow metal sphere?
2. How does the distribution of excess electrons affect the electric field?
3. What is Gauss’s Law and how does it apply to different geometries?
4. How does the electric field behave inside a solid conducting sphere?
5. How would the electric field change if the sphere were not a conductor?

Tip: In electrostatics, a charged conductor's interior always has zero electric field due to the cancellation of forces from symmetrical charge distribution.