When electric field is applied inside a conductor then free electron are accelerated. Their average velocity in time interval t is proportional to

Options

A. `t^(1)`
B. `t^(2)`
C. `sqrt(t)`
D. `t^(0 )`

Answer

To solve the problem of how the average velocity of free electrons in a conductor is affected by an applied electric field, we can follow these steps:

### Step 1: Understand the Concept of Drift Velocity
When an electric field is applied to a conductor, free electrons within the conductor experience a force and begin to accelerate. This results in a net movement of electrons in the opposite direction of the electric field, known as drift velocity (Vd).

**Hint:** Recall that drift velocity is the average velocity of charge carriers (electrons) in a conductor due to an applied electric field.

### Step 2: Define Drift Velocity
The drift velocity (Vd) can be expressed in terms of the mobility (μ) of the electrons and the electric field (E) applied. The relationship is given by:
\[ V_d = \mu E \]

**Hint:** Mobility (μ) is a measure of how quickly an electron can move through a conductor when subjected to an electric field.

### Step 3: Analyze the Dependence on Time
The drift velocity depends on the mobility of the electrons and the strength of the electric field, but it does not depend on the time interval (t) over which the electric field is applied. This means that the average velocity of the electrons remains constant regardless of how long the electric field is applied.

**Hint:** Consider that the drift velocity is a steady-state velocity that does not change with time once the electric field is applied.

### Step 4: Conclude the Relationship
Since the drift velocity does not depend on time, we can express this relationship mathematically:
\[ V_d \propto t^0 \]
This indicates that the average velocity is proportional to \( t^0 \), which equals 1, meaning it is constant.

**Hint:** Remember that any quantity raised to the power of zero is equal to one, indicating no dependence on that variable.

### Final Answer
The average velocity of free electrons in a conductor when an electric field is applied is proportional to \( t^0 \).

**Answer:** \( V_d \propto t^0 \) (Option 4)