A uniform electric field of 20 N/C exists in the vertically downward direction. Find the increase in the electric potential as one goes up through a height of 40 cm.

Options

A. 8 VOLTS
B. -8 VOLTS
C. 0 VOLTS
D. NONE OF THESE

Explanation

To solve the problem of finding the increase in electric potential as one moves up through a height of 40 cm in a uniform electric field of 20 N/C directed downward, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Electric field \( E = 20 \, \text{N/C} \) (downward).
- Height \( h = 40 \, \text{cm} = 0.40 \, \text{m} \).

2. **Understand the Relationship Between Electric Field and Electric Potential**:
- The relationship between electric field \( E \) and electric potential \( V \) is given by:
\[ E = -\frac{dV}{dr} \]
- This implies that the change in electric potential \( \Delta V \) can be expressed as:
\[ \Delta V = -E \cdot \Delta r \]
- Here, \( \Delta r \) is the displacement in the direction of the field.

3. **Determine the Direction of Displacement**:
- Since the electric field is directed downward, moving upward (against the field) means that \( \Delta r \) will be positive in the upward direction. Therefore, we can consider \( \Delta r = +0.40 \, \text{m} \).

4. **Calculate the Change in Electric Potential**:
- Substitute the values into the equation:
\[ \Delta V = -E \cdot \Delta r = -20 \, \text{N/C} \cdot 0.40 \, \text{m} \]
- Performing the multiplication:
\[ \Delta V = -20 \cdot 0.40 = -8 \, \text{V} \]

5. **Interpret the Result**:
- The negative sign indicates that the potential decreases as one moves upward against the electric field. However, since the question asks for the increase in potential, we take the absolute value:
\[ \text{Increase in Electric Potential} = 8 \, \text{V} \]

### Final Answer:
The increase in electric potential as one goes up through a height of 40 cm is **8 volts**.

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