The magnitude of the electric field within a conducting wire depends on which of the following quantities?

Options

A. Potential difference, wire diameter, wire length, and wire conductivity
B. Potential ditorence and wire conductivity only
C. Potential difference, wire length, and wire conductivity only
D. Wire diameter, wire length, and wire conductivity only

Answer

To determine the magnitude of the electric field within a conducting wire, we can follow these steps:

### Step 1: Understand the Formula for Electric Field
The electric field (E) can be expressed using the formula:
\[ E = \frac{V}{L} \]
where \( V \) is the potential difference across the wire and \( L \) is the length of the wire.

### Step 2: Identify the Factors Affecting Electric Field
From the formula, we can see that the electric field depends on:
1. **Potential Difference (V)**: The voltage applied across the wire.
2. **Length of the Wire (L)**: The distance over which the potential difference is applied.

### Step 3: Consider Conductivity
In addition to potential difference and length, the conductivity of the wire also plays a role. Conductivity affects how easily charges can move through the wire, which in turn influences the electric field. A more conductive wire will allow a higher electric field for the same potential difference and length.

### Step 4: Summarize the Dependencies
Thus, the magnitude of the electric field within a conducting wire depends on:
- The potential difference (V)
- The length of the wire (L)
- The conductivity of the wire (σ)

### Conclusion
Therefore, the correct answer is that the electric field within a conducting wire depends on the potential difference, the length of the wire, and the conductivity of the wire.