There is one metallic rod AB whose area of cross section decreases from its end A towards the end B. End A of the rod is connected to positive terminal of a battery and end B is connected to its negative terminal. If one moves in a direction from B to A,

Options

A. the magnitude of the current will increase
B. the magnitude of current will decrease
C. the magnitude of drift velocity will decrease
D. the magnitude of drift velocity will increase

Explanation

To solve the problem step by step, we will analyze the situation of the metallic rod AB with a decreasing cross-sectional area from end A to end B, which is connected to a battery.

### Step 1: Understanding the Setup
- We have a metallic rod AB where the area of cross-section decreases from A to B.
- End A is connected to the positive terminal of a battery, and end B is connected to the negative terminal.

**Hint:** Visualize the rod and the direction of current flow from A to B.

### Step 2: Current Flow in the Rod
- When current flows through the rod, the same amount of charge must flow through any cross-section of the rod at any point in time due to the conservation of charge.
- Therefore, the current (I) remains constant throughout the rod.

**Hint:** Remember that current is the flow of charge and is conserved in a closed circuit.

### Step 3: Analyzing Cross-Sectional Area
- As we move from B to A, the cross-sectional area (A) of the rod increases.
- The relationship between current (I), charge density (n), charge (e), area (A), and drift velocity (Vd) is given by the equation:
\[ I = n \cdot e \cdot A \cdot V_d \]

**Hint:** Identify how the area affects the drift velocity in the equation.

### Step 4: Finding Drift Velocity
- Rearranging the equation gives:
\[ V_d = \frac{I}{n \cdot e \cdot A} \]
- Since I is constant and n (number density of charge carriers) and e (charge of an electron) are also constants, we can see that drift velocity (Vd) is inversely proportional to the area (A).
- As we move from B to A, since A is increasing, Vd must decrease.

**Hint:** Focus on the inverse relationship between drift velocity and area.

### Step 5: Conclusion
- Therefore, the magnitude of the drift velocity will decrease as we move from B to A.

**Final Answer:** The magnitude of drift velocity will decrease.