The electric field lines coming out of an equipotential surface are

Options

A. perpendicular to the surface
B. parallel to the surface
C. in all directions
D. zero

Explanation

To solve the question regarding the electric field lines coming out of an equipotential surface, we can follow these steps:

### Step 1: Understand the concept of an equipotential surface
An equipotential surface is defined as a surface on which the electric potential is the same at every point. This means that no work is done when moving a charge along this surface.

**Hint:** Recall that an equipotential surface has constant potential, so the potential difference between any two points on the surface is zero.

### Step 2: Analyze the relationship between electric field and equipotential surfaces
The electric field (E) is related to the potential (V) by the equation:
\[ E = -\nabla V \]
This implies that the electric field points in the direction of the greatest decrease of potential.

**Hint:** Remember that the electric field is always directed from regions of higher potential to lower potential.

### Step 3: Determine the orientation of electric field lines
Since the electric field lines represent the direction of the electric field, they must be perpendicular to the equipotential surface. If they were not perpendicular, it would imply that there is a potential difference along the surface, which contradicts the definition of an equipotential surface.

**Hint:** Visualize the electric field lines as arrows that must intersect the equipotential surface at right angles.

### Step 4: Conclude the relationship
Based on the above analysis, we can conclude that the electric field lines coming out of an equipotential surface are always perpendicular to that surface.

**Final Answer:** The electric field lines coming out of an equipotential surface are perpendicular to the surface.