Which of the following diagram represents the variation of electric field vector with time for a circularly polarised light?

Options

A.
B.
C.
D.

Explanation

To determine which diagram represents the variation of the electric field vector with time for circularly polarized light, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Circular Polarization**:
Circularly polarized light consists of two perpendicular electric field components that oscillate in phase with a phase difference of \( \frac{\pi}{2} \) (90 degrees). This means that one component can be represented by a sine function and the other by a cosine function.

2. **Defining the Electric Field Components**:
- Let the first electric field component be \( E_1 = E_0 \sin(\omega t) \).
- Let the second electric field component be \( E_2 = E_0 \cos(\omega t) \).

3. **Analyzing the Components**:
- The two components \( E_1 \) and \( E_2 \) are perpendicular to each other. This is a key characteristic of circularly polarized light.

4. **Resultant Electric Field**:
- The resultant electric field \( E \) can be expressed as:
\[ E = \sqrt{E_1^2 + E_2^2} = \sqrt{(E_0 \sin(\omega t))^2 + (E_0 \cos(\omega t))^2} \]
- This simplifies to:
\[ E = E_0 \]
- The amplitude remains constant over time, indicating that the magnitude of the electric field does not change.

5. **Graphical Representation**:
- The variation of the electric field vector with time will show a circular motion when plotted in a 2D plane. The electric field vector will rotate in a circular path, maintaining a constant amplitude.

6. **Identifying the Correct Diagram**:
- The correct diagram will show the electric field vector rotating in a circular manner, indicating that it is continuously changing direction while maintaining a constant magnitude.

### Conclusion:
The diagram that represents the variation of the electric field vector with time for circularly polarized light will show a circular path, confirming that the electric field vectors are perpendicular and oscillate with a phase difference of \( \frac{\pi}{2} \).