Angle between equipotential surface and lines of force is

Options

A. zero
B. `180^(@)`
C. `90^(@)`
D. `45^(@)`

Answer

To solve the question regarding the angle between equipotential surfaces and lines of force, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equipotential Surfaces**:
- Equipotential surfaces are defined as surfaces where the electric potential is constant. This means that if you move along an equipotential surface, there is no change in electric potential (ΔV = 0).

2. **Understanding Electric Field Lines**:
- Electric field lines represent the direction of the electric field. The electric field (E) points in the direction in which a positive test charge would move.

3. **Analyzing the Angle**:
- Let's denote the angle between the electric field lines and the equipotential surface as θ.
- If the electric field makes an angle θ with the normal (perpendicular) to the equipotential surface, we can analyze the components of the electric field.

4. **Components of Electric Field**:
- The electric field can be resolved into two components: one parallel to the equipotential surface (E_parallel = E cos θ) and one perpendicular to the equipotential surface (E_perpendicular = E sin θ).

5. **Condition for Equipotential Surface**:
- For the surface to remain equipotential, the potential must not change as you move along the surface. This means that the component of the electric field parallel to the surface (E_parallel) must be zero.
- Therefore, we have:
\[ E \cos θ = 0 \]
- The only way for this equation to hold true is if cos θ = 0, which occurs when θ = 90 degrees.

6. **Conclusion**:
- Hence, the angle between the equipotential surface and the electric field lines (lines of force) is 90 degrees. This means that the electric field lines are always perpendicular to the equipotential surfaces.

### Final Answer:
The angle between equipotential surfaces and lines of force is **90 degrees**.

---