Equipotential surfaces associated with a uniform electric field along positive x-axis are planes parallel to

Options

A. y-z plane
B. x-y plane
C. x-z plane
D. Any plane parallel to x-axis

Answer

To solve the question regarding the equipotential surfaces associated with a uniform electric field along the positive x-axis, we can follow these steps:

### Step 1: Understand the Concept of Equipotential Surfaces
Equipotential surfaces are defined as surfaces where the electric potential is constant. This means that no work is done when moving a charge along an equipotential surface.

**Hint:** Remember that the electric potential difference between any two points on an equipotential surface is zero.

### Step 2: Identify the Direction of the Electric Field
The problem states that the electric field is uniform and directed along the positive x-axis. This means that the electric field vector \( \vec{E} \) points in the positive x-direction.

**Hint:** Visualize the electric field direction to better understand how it relates to equipotential surfaces.

### Step 3: Determine the Orientation of Equipotential Surfaces
Equipotential surfaces are always perpendicular to the direction of the electric field. Since the electric field is along the positive x-axis, the equipotential surfaces must be oriented in such a way that they are perpendicular to this direction.

**Hint:** Think about how planes can be oriented in three-dimensional space relative to the x-axis.

### Step 4: Analyze the Options Given
The options provided are:
1. yz plane
2. xy plane
3. xz plane
4. Any plane parallel to the x-axis

The yz plane consists of all points where the x-coordinate is constant, meaning it is perpendicular to the x-axis.

**Hint:** Consider which planes would maintain a constant potential while being perpendicular to the electric field direction.

### Step 5: Conclude the Correct Answer
Since the equipotential surfaces must be perpendicular to the electric field along the x-axis, the correct answer is that the equipotential surfaces are planes parallel to the yz plane.

**Final Answer:** The correct option is **1. yz plane**.