The electric and magnetic field of an electromagnetic wave is

Options

A. in phase and perpendicular to each other
B. in phase and parallel to each other
C. in opposite phase and perpendicular to each other
D. in opposite phase and parallel to each other

Explanation

To solve the problem regarding the electric and magnetic fields of an electromagnetic wave, we will follow these steps:

### Step 1: Understand the Representation of Electromagnetic Waves
The electric field (E) and magnetic field (B) of an electromagnetic wave can be represented mathematically as:
- Electric Field: \( E = E_0 \sin(\omega t - kx) \)
- Magnetic Field: \( B = B_0 \sin(\omega t - kx) \)

### Step 2: Identify the Directions of the Fields
In an electromagnetic wave:
- The electric field (E) oscillates in one direction (let's say the x-direction).
- The magnetic field (B) oscillates in a direction perpendicular to the electric field (let's say the y-direction).
- The direction of wave propagation is perpendicular to both the electric and magnetic fields (let's say the z-direction).

### Step 3: Confirm the Perpendicularity of the Fields
According to the properties of electromagnetic waves:
- The electric field is perpendicular to the magnetic field.
- Both the electric field and magnetic field are perpendicular to the direction of wave propagation.
This can be summarized as:
- \( E \perp B \)
- \( E \perp \text{Wave Direction} \)
- \( B \perp \text{Wave Direction} \)

### Step 4: Analyze the Phase Relationship
The electric field and magnetic field oscillate in phase, meaning they reach their maximum and minimum values at the same time:
- The phase of the electric field and magnetic field is the same.

### Step 5: Conclusion
From the above analysis, we can conclude that:
- The electric field and magnetic field of an electromagnetic wave are perpendicular to each other and in phase.

Thus, the correct answer to the question is that the electric field and magnetic field of an electromagnetic wave are in phase and perpendicular to each other.