Electric potential difference between the positive plate and halfway point between the two parallel plates of a fully charged capacitor is

Options

A. Zero
B. One half of the total potential difference between the two plates
C. One quarter of the total potential difference between the two plates
D. None of the above

Answer

To solve the problem of finding the electric potential difference between the positive plate and the halfway point between the two parallel plates of a fully charged capacitor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- A capacitor consists of two parallel plates: one positively charged and the other negatively charged. Let's denote the total potential difference between the two plates as \( V \).

2. **Identify the Halfway Point**:
- The halfway point between the two plates is located at the midpoint of the distance separating the plates.

3. **Electric Field in a Capacitor**:
- The electric field \( E \) between the plates of a parallel plate capacitor is uniform and can be expressed as:
\[ E = \frac{V}{d} \]
where \( d \) is the distance between the plates.

4. **Potential Difference Calculation**:
- The potential difference \( V' \) between the positive plate and the halfway point can be calculated using the formula for potential difference, which is the product of the electric field and the distance:
\[ V' = E \cdot \left(\frac{d}{2}\right) \]
- Substituting the expression for \( E \):
\[ V' = \left(\frac{V}{d}\right) \cdot \left(\frac{d}{2}\right) \]
- Simplifying this gives:
\[ V' = \frac{V}{2} \]

5. **Conclusion**:
- The electric potential difference between the positive plate and the halfway point is half of the total potential difference \( V \). Therefore, the answer is:
\[ \text{Electric potential difference} = \frac{V}{2} \]

### Final Answer:
The electric potential difference between the positive plate and the halfway point between the two parallel plates of a fully charged capacitor is **one half of the total potential difference between the two plates**.