A Steady current flows in a metalic conductor of non uniform cross section. The quantity/quantities which remain constant along the length of the conductor is/are

Options

A. current, electric field and drift speed
B. drift speed only
C. current and drift speed
D. current only

Explanation

To solve the problem, we need to analyze the situation of a steady current flowing through a metallic conductor with a non-uniform cross-section. We will identify which quantities remain constant along the length of the conductor.

### Step-by-Step Solution:

1. **Understanding the Concept of Steady Current**:
- A steady current means that the amount of charge flowing through any cross-section of the conductor per unit time is constant. Therefore, the current (I) remains constant throughout the conductor.

**Hint**: Recall the definition of steady current and how it relates to charge flow.

2. **Analyzing the Cross-Sectional Area**:
- The conductor has a non-uniform cross-section, meaning that the area (A) changes along the length of the conductor. For example, let’s denote two cross-sections as A1 and A2, where A2 > A1.

**Hint**: Visualize the conductor and note how the area changes along its length.

3. **Current Density and Drift Speed**:
- The current density (J) is defined as J = I/A. Since the current (I) is constant and the area (A) varies, the current density will change with the area. Specifically, as the area decreases, the current density increases, and vice versa.
- The drift speed (Vd) of the charge carriers is given by the formula Vd = I/(nqA), where n is the number of charge carriers per unit volume and q is the charge of the carriers. Since A changes, Vd will also change.

**Hint**: Remember how current density and drift speed are related to the area of the conductor.

4. **Electric Field in the Conductor**:
- According to Ohm's law, the electric field (E) in the conductor can be expressed as E = J/σ, where σ is the conductivity. Since J is dependent on the area (as shown above), the electric field will also vary along the length of the conductor.

**Hint**: Consider how Ohm's law relates current density to electric field and how area affects both.

5. **Conclusion**:
- From the analysis, we conclude that the only quantity that remains constant along the length of the conductor is the current (I). The drift speed (Vd) and the electric field (E) will vary due to the changes in cross-sectional area.

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

### Summary of Constant Quantities:
- **Constant Quantity**: Current (I)
- **Variable Quantities**: Drift speed (Vd) and Electric field (E)