The drift velocity does not depend upon

Options

A. cross-section of the wire
B. length of the wire
C. number of the free electrons
D. magnitude of the current

Answer

To determine which factor does not affect the drift velocity of electrons in a conductor, we can analyze the relationship between drift velocity and other parameters using the formula for current.

### Step-by-Step Solution:

1. **Understand the Formula for Current**:
The current (I) in a conductor can be expressed using the formula:
\[ I = n \cdot e \cdot A \cdot v_d \]
where:
- \( I \) = current
- \( n \) = number density of free electrons (number of free electrons per unit volume)
- \( e \) = charge of an electron
- \( A \) = cross-sectional area of the wire
- \( v_d \) = drift velocity of the electrons

2. **Rearranging the Formula for Drift Velocity**:
From the formula, we can rearrange it to express drift velocity:
\[ v_d = \frac{I}{n \cdot e \cdot A} \]
This shows that drift velocity is directly proportional to the current and inversely proportional to the number density of free electrons, the charge of the electron, and the cross-sectional area of the wire.

3. **Analyze the Dependence**:
- **Cross-sectional Area (A)**: Drift velocity depends on this because an increase in area decreases the drift velocity for a constant current.
- **Number of Free Electrons (n)**: Drift velocity also depends on this; more free electrons mean a lower drift velocity for a given current.
- **Magnitude of Current (I)**: Drift velocity is directly proportional to current; increasing current increases drift velocity.
- **Length of the Wire**: The length of the wire does not appear in the formula for drift velocity. It does not affect the drift velocity directly.

4. **Conclusion**:
Based on the analysis, the drift velocity does not depend on the length of the wire. Therefore, the correct answer is:
\[ \text{Option 2: Length of the wire} \]