A cylindrical copper conductor AB length `L` areaa of cross-section a has large number of free electrons which at mean temperature move at random within the body of the conductor like the molecules of a gas. The average thermal motion at room temperature is of the enter of `10^(5)ms^(-1)` where a potential difference `V` is applied free electronic in the condictior experience , the free electrons in the conductor experience force and are accelerated towards the positive emf of the condutor on their gained kinetic energy After each collision the free electronic are angle acceleration due of the electric field , towards the positive end the conductor and next collision with the ions/atoms of the electrons The average speed of the free electrons with which they drift toward the positive and of the conductor under the effect of applied electric field is called drift of the electrons
When the potential difference is applied the two ends of the conductors , an electric field exists

Options

A. outside the conductor
B. inside the conductor
C. both outside and inside the conductor
D. no where

Explanation

To solve the question, we need to analyze the behavior of free electrons in a cylindrical copper conductor when a potential difference is applied across its ends. Here’s a step-by-step solution:

### Step 1: Understanding the System
We have a cylindrical copper conductor named AB with length \( L \) and cross-sectional area \( A \). At room temperature, free electrons in the conductor move randomly with an average thermal speed of \( 10^5 \, \text{m/s} \).

**Hint:** Remember that the random motion of electrons is similar to gas molecules, but when an electric field is applied, they experience a net drift.

### Step 2: Applying Potential Difference
When a potential difference \( V \) is applied across the ends of the conductor, an electric field \( E \) is established inside the conductor. This electric field causes the free electrons to experience a force and drift towards the positive terminal.

**Hint:** The relationship between potential difference and electric field can be expressed as \( E = \frac{V}{L} \).

### Step 3: Drift Speed of Electrons
The average speed at which the electrons drift towards the positive end of the conductor under the influence of the electric field is known as the drift speed. The drift speed \( v_d \) can be expressed using the formula:
\[ v_d = \frac{eE\tau}{m} \]
where:
- \( e \) is the charge of an electron,
- \( E \) is the electric field,
- \( \tau \) is the relaxation time (average time between collisions),
- \( m \) is the mass of an electron.

**Hint:** The drift speed is significantly lower than the random thermal speed of the electrons due to the frequent collisions with the lattice ions.

### Step 4: Location of Electric Field
The question asks where the electric field exists when the potential difference is applied across the conductor. The electric field exists inside the conductor, as it is the region where the free electrons are influenced by the applied electric field.

**Hint:** Consider the behavior of electric fields in conductors; they are established in the region where charges can move freely.

### Conclusion
Thus, when a potential difference is applied across the cylindrical conductor, the electric field exists **inside the conductor**.

### Final Answer
The correct option is: **Inside the conductor.**