A cross a metallic conductor of non-uniform cross-section, a constant potential difference is applied. The quantity which remain (s) constant along the conductor is

Options

A. current density
B. current
C. drift velocity
D. electric field

Answer

To solve the question regarding the quantities that remain constant across a metallic conductor of non-uniform cross-section with a constant potential difference applied, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a metallic conductor with a non-uniform cross-section.
- A constant potential difference (V) is applied across the length of the conductor.

2. **Identifying the Relevant Quantities**:
- The quantities we need to consider are:
- Current (I)
- Current Density (J)
- Drift Velocity (v_d)
- Electric Field (E)

3. **Current (I)**:
- The current (I) is defined as the rate of flow of charge. Since there is no accumulation of charge in a steady state, the current remains constant throughout the conductor.
- Thus, **I is constant**.

4. **Current Density (J)**:
- Current density (J) is defined as \( J = \frac{I}{A} \), where A is the cross-sectional area.
- Since the cross-sectional area (A) varies along the length of the conductor, the current density will also vary.
- Therefore, **J is not constant**.

5. **Drift Velocity (v_d)**:
- Drift velocity is given by \( v_d = \frac{I}{nAe} \), where n is the number of charge carriers per unit volume and e is the charge of an electron.
- As the area A changes, the drift velocity will also change, since I is constant but A varies.
- Hence, **v_d is not constant**.

6. **Electric Field (E)**:
- The electric field can be expressed as \( E = \frac{V}{L} \), where L is the length of the conductor.
- However, since the area A is changing, the resistance (R) which is given by \( R = \frac{\rho L}{A} \) will also change, affecting the potential difference across different sections.
- Therefore, **E is not constant**.

### Conclusion:
The only quantity that remains constant along the conductor is the **current (I)**.

### Final Answer:
The quantity that remains constant along the conductor is the **current (I)**.

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