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This problem involves calculating the electric field (E) and electric potential (V) at a point inside a spherical conductor, which has a radius of 9 cm and is charged with a total charge of 6 mC (milliCoulombs). 

### Step-by-Step Explanation:

1. **Given Information:**
   - Radius of the spherical conductor \( R = 9 \, \text{cm} = 0.09 \, \text{m} \)
   - Charge \( Q = 6 \, \text{mC} = 6 \times 10^{-3} \, \text{C} \)
   - The point at which we're calculating is at 3 cm from the center, so \( r = 3 \, \text{cm} = 0.03 \, \text{m} \).

2. **Concepts to Apply:**
   - **Electric Field Inside a Conductor**: For a conductor, the electric field inside the conductor (at any point inside the radius \( R \)) is always zero:
     \[
     E = 0 \, \text{N/C} \quad \text{(inside a conductor)}
     \]
   - **Electric Potential Inside a Conductor**: The electric potential inside the conductor is the same as the potential at the surface of the sphere. The potential on the surface is given by:
     \[
     V = \frac{k Q}{R}
     \]
     where \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \) is Coulomb's constant, \( Q \) is the charge, and \( R \) is the radius of the sphere.

3. **Calculations**:

   - **Electric Field**:
     Since the point of interest is inside the spherical conductor at \( r = 0.03 \, \text{m} \), the electric field:
     \[
     E = 0 \, \text{N/C}
     \]

   - **Electric Potential**:
     Using the formula for the potential on the surface of a sphere:
     \[
     V = \frac{(9 \times 10^9) \times (6 \times 10^{-3})}{0.09} = 6 \times 10^5 \, \text{V}
     \]

4. **Answer**:
   - The electric field at 3 cm from the center is \( E = 0 \, \text{N/C} \).
   - The potential at 3 cm from the center is \( V = 6 \times 10^5 \, \text{V} \).
   
   Therefore, the correct answer is:
   \[
   \boxed{b. \, E = \text{nol}, \, V = 6 \times 10^5 \, \text{volt}}
   \]

Would you like more details or have any other questions? Here are some related questions you might find useful:

1. What is the electric field outside a spherical conductor?
2. How does electric potential change with distance inside a conductor?
3. What happens to the electric field if the charge distribution is non-uniform?
4. How can Gauss's law be applied to find the electric field in different regions of a conductor?
5. How is electric potential related to the work done by an electric force?

**Tip:** Inside a conductor, the electric field is always zero, but the potential remains constant throughout the volume!

A spherical conductor with a radius of 9 cm is given a charge of 6 mC. What are the electric field and potential at a point 3 cm from the center?

This problem involves calculating the electric field and potential inside a spherical conductor with a radius of 9 cm and charge of 6 mC. Learn how to apply Gauss's law and the properties of conductors to determine that the electric field is zero and the potential is 6 x 10^5 V at 3 cm from the center.

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