A potential barrier of `0.50 V` exists across a `P-N` junction. If the depletion region is `5.0xx10^(-7)m`, wide the intensity of the electric field in this region is

Options

A. `10^6` V/m
B. `10^7` V/m
C. `10^5` V/m
D. `10^4` V/m

Explanation

To find the intensity of the electric field in the depletion region of a P-N junction, we can use the relationship between the potential barrier (V), the electric field (E), and the width of the depletion region (r). The formula we will use is:

\[ V = E \cdot r \]

Where:
- \( V \) is the potential barrier (in volts),
- \( E \) is the electric field intensity (in volts per meter),
- \( r \) is the width of the depletion region (in meters).

### Step-by-Step Solution:

1. **Identify the given values**:
- Potential barrier, \( V = 0.50 \, \text{V} \)
- Width of the depletion region, \( r = 5.0 \times 10^{-7} \, \text{m} \)

2. **Rearrange the formula to solve for electric field (E)**:
\[ E = \frac{V}{r} \]

3. **Substitute the known values into the equation**:
\[ E = \frac{0.50 \, \text{V}}{5.0 \times 10^{-7} \, \text{m}} \]

4. **Calculate the electric field**:
\[ E = \frac{0.50}{5.0 \times 10^{-7}} = 1.0 \times 10^{6} \, \text{V/m} \]

5. **Final answer**:
The intensity of the electric field in the depletion region is:
\[ E = 1.0 \times 10^{6} \, \text{V/m} \]