Variation in potential is maximum if one goes.

Options

A. along the line of force.
B. Perpendicular to the line of force.
C. in any direction.
D. none of these.

Explanation

To solve the question regarding the variation in electric potential, we will analyze the relationship between electric potential and electric field.

### Step-by-Step Solution:

1. **Understanding the Concept of Electric Potential (V)**:
Electric potential is a measure of the potential energy per unit charge at a point in an electric field. The variation in potential (dV) can be related to the electric field (E) and the displacement (dr) through the formula:
\[ dV = -\int E \cdot dr \]

2. **Dot Product and Angle**:
The dot product in the equation can be expressed as:
\[ dV = -E \, dr \, \cos(\theta) \]
where \( \theta \) is the angle between the electric field vector (E) and the displacement vector (dr).

3. **Maximizing the Variation in Potential**:
To maximize the variation in potential (dV), we need to maximize the term \( \cos(\theta) \). The maximum value of \( \cos(\theta) \) is 1, which occurs when:
\[ \theta = 0^\circ \]
This means that the displacement (dr) must be in the same direction as the electric field (E).

4. **Conclusion**:
Since the variation in potential is maximum when the angle \( \theta \) is 0 degrees, this indicates that the path taken must be along the direction of the electric field lines (line of force). Therefore, the correct answer to the question is:
\[ \text{The variation in potential is maximum if one goes along the line of force.} \]

### Final Answer:
The correct option is **A: along the line of force**.