An electromagnetic wave consists of oscillating electric and magnetic fields. What is the phase relationship between these fields?

Options

A. `pi`
B. `(pi)/(2)`
C. `(pi)/(4)`
D. Zero

Answer

To determine the phase relationship between the oscillating electric and magnetic fields in an electromagnetic wave, we can follow these steps:

### Step 1: Understand the Direction of Propagation
An electromagnetic wave travels in a specific direction. For this explanation, let's assume the wave is traveling in the x-direction.

**Hint:** Identify the direction of wave propagation to understand the orientation of electric and magnetic fields.

### Step 2: Identify the Orientation of Electric and Magnetic Fields
For an electromagnetic wave traveling in the x-direction:
- The electric field (E) oscillates in the y-direction.
- The magnetic field (B) oscillates in the z-direction.

**Hint:** Remember that the electric field and magnetic field are always perpendicular to each other and to the direction of wave propagation.

### Step 3: Write the Equations for Electric and Magnetic Fields
The electric field can be represented as:
\[ E = E_0 \sin(\omega t - kx) \]
where \( E_0 \) is the amplitude, \( \omega \) is the angular frequency, and \( k \) is the wave number.

The magnetic field can be represented as:
\[ B = B_0 \sin(\omega t - kx) \]
where \( B_0 \) is the amplitude of the magnetic field.

**Hint:** The sine function indicates that both fields oscillate sinusoidally over time and space.

### Step 4: Analyze the Phase of Both Fields
From the equations, we see that both the electric field and magnetic field have the same phase term, which is \( \omega t - kx \).

**Hint:** Compare the arguments of the sine functions to determine the phase relationship.

### Step 5: Determine the Phase Difference
Since both fields have the same phase term, the phase difference between the electric field and the magnetic field is:
\[ \text{Phase Difference} = 0 \]

**Hint:** A phase difference of 0 means that both fields reach their maximum and minimum values simultaneously.

### Conclusion
The phase relationship between the electric and magnetic fields in an electromagnetic wave is that they are in phase, with a phase difference of 0.

**Final Answer:** The phase difference between the electric and magnetic fields in an electromagnetic wave is 0.