Assertion : Current flows in a conductor only when there is an external electric field within the conductor.
Reason: The drift velocity of the electrons is directly proportional to the electric field.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

**Assertion:** Current flows in a conductor only when there is an external electric field within the conductor.

**Reason:** The drift velocity of the electrons is directly proportional to the electric field.

### Step-by-Step Solution:

1. **Understanding Current Flow in Conductors:**
- In a conductor, there are free electrons that move randomly in all directions when no external electric field is applied. This random motion results in no net current flow because the velocities cancel each other out.

**Hint:** Remember that current is the flow of charge, and if charges are moving randomly, there is no net flow.

2. **Effect of an External Electric Field:**
- When an external electric field is applied, it influences the motion of these free electrons. Instead of moving randomly, the electrons start to drift in a specific direction due to the force exerted on them by the electric field.

**Hint:** Consider how forces affect the motion of charged particles in an electric field.

3. **Drift Velocity:**
- The drift velocity of electrons is defined as the average velocity that a charge carrier, such as an electron, attains due to an electric field. The drift velocity (v_d) is directly proportional to the electric field (E) applied across the conductor, which can be expressed as:
\[ v_d \propto E \]
- This means that as the electric field increases, the drift velocity of the electrons also increases.

**Hint:** Recall the relationship between drift velocity and electric field; it’s a key concept in understanding current flow.

4. **Conclusion on Assertion and Reason:**
- Since the assertion states that current flows only when there is an external electric field, and the reason correctly explains that this is due to the drift velocity being proportional to the electric field, both the assertion and reason are true.
- Furthermore, the reason provides a correct explanation for the assertion.

**Hint:** Always check if the reason logically supports the assertion when evaluating their truth.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.