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To solve this problem, we need to analyze how the electric potential \( V(r) \) behaves as a function of distance \( r \) from the center of an isolated conducting sphere of radius \( R \) with charge \( +Q \).

### Key points to remember:
1. **Inside the sphere** \( (r < R) \):
   - The potential inside a conducting sphere is constant and equal to the value at the surface. This is because the electric field inside a conductor in electrostatic equilibrium is zero.
   - Therefore, for \( r \leq R \), \( V(r) \) is constant and equal to the potential on the surface of the sphere \( V(R) \).

2. **Outside the sphere** \( (r \geq R) \):
   - The sphere behaves like a point charge at its center. The potential at a distance \( r \) from the center of the sphere is given by:
     \[
     V(r) = \frac{kQ}{r}
     \]
   - This implies that the potential decreases inversely with distance for \( r > R \).

### Which graph matches this behavior?
- **Graph (3)**: This graph shows a constant potential from \( r = 0 \) to \( r = R \), and then the potential decreases as \( 1/r \) for \( r > R \), which matches the expected behavior.

Thus, **the correct graph is (3)**.

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Would you like more details, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. How is the electric field related to the potential outside a conducting sphere?
2. What is the electric potential inside a solid non-conducting sphere?
3. How does the potential behave if the charge distribution were not uniform?
4. What happens to the potential if the sphere is grounded?
5. How does the potential change if the sphere were negatively charged instead of positively?

**Tip:** Electric potential is a scalar quantity, meaning it does not have direction but only magnitude, simplifying its calculation compared to vector quantities like electric field.

An isolated conducting sphere of radius R has a charge +Q. Which graph best represents the electric potential (V) as a function of r, the distance from the center of the sphere?

This problem explores the electric potential around a conducting sphere with charge +Q as a function of distance from its center. It uses key electrostatic principles like constant potential inside a conductor and the inverse relationship of potential with distance outside the sphere. Suitable for undergraduate physics students.

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