A stready current i is flowing through a conductor of uniform cross-section. Any segment of the conductor has

Options

A. zero charge
B. only positive charge
C. only negative charge
D. charge proportional to current `i`

Answer

To solve the problem, we need to analyze the behavior of charge in a conductor through which a steady current \( I \) is flowing. Here’s a step-by-step solution:

### Step 1: Understanding Current
Current (\( I \)) is defined as the rate of flow of charge. Mathematically, it is given by:
\[ I = \frac{dQ}{dt} \]
where \( dQ \) is the amount of charge flowing through a cross-section of the conductor in a small time interval \( dt \).

**Hint:** Remember that current is the flow of charge per unit time.

### Step 2: Charge Flow in a Conductor
In a steady state, the current flowing into any segment of the conductor must equal the current flowing out of that segment. This means:
\[ I_{\text{in}} = I_{\text{out}} = I \]

**Hint:** Think about the conservation of charge – what goes in must come out in a steady current.

### Step 3: Analyzing Charge in a Segment
Let’s consider a small segment of the conductor. If we denote the charge entering the segment as \( Q_{\text{in}} \) and the charge leaving as \( Q_{\text{out}} \), we can express these charges in terms of current:
\[ Q_{\text{in}} = I \cdot t \quad \text{and} \quad Q_{\text{out}} = I \cdot t \]
for a time duration \( t \).

**Hint:** Relate the charge to the current using the time duration for which the current flows.

### Step 4: Net Charge in the Segment
The net charge (\( Q_{\text{net}} \)) in the segment can be calculated as:
\[ Q_{\text{net}} = Q_{\text{out}} - Q_{\text{in}} = (I \cdot t) - (I \cdot t) = 0 \]

**Hint:** Consider what happens when you subtract equal quantities.

### Step 5: Conclusion
Since the net charge in any segment of the conductor is zero, we conclude that:
- Any segment of the conductor has no excess charge at any moment.

**Final Answer:** The net charge in any segment of the conductor is zero.