In electromagnetic wave, the phase difference between electric and magnetic field vectors E and B is

Options

A. zero
B. `pi//2`
C. `pi`
D. `pi//4`

Answer

To solve the question regarding the phase difference between the electric field vector (E) and the magnetic field vector (B) in an electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Propagation of Electromagnetic Waves**:
- In an electromagnetic wave, the electric field (E) and magnetic field (B) oscillate perpendicular to each other and to the direction of wave propagation.
- For example, if the electric field oscillates in the Y direction and the magnetic field oscillates in the Z direction, then the wave propagates in the X direction.

2. **Write the Equations for E and B**:
- The electric field can be represented as:
\[ E = E_0 \sin(\omega t - kx) \]
- The magnetic field can be represented as:
\[ B = B_0 \sin(\omega t - kx) \]
- Here, \(E_0\) and \(B_0\) are the amplitudes of the electric and magnetic fields, respectively, \(\omega\) is the angular frequency, \(t\) is time, \(k\) is the wave number, and \(x\) is the position.

3. **Analyze the Phase of Both Fields**:
- Both the electric field E and the magnetic field B have the same functional form: they both depend on \((\omega t - kx)\).
- This indicates that both fields reach their maximum and minimum values at the same time.

4. **Determine the Phase Difference**:
- The phase difference \(\Delta \phi\) between two sinusoidal functions of the same frequency is given by:
\[ \Delta \phi = \phi_E - \phi_B \]
- Since both E and B have the same phase term \((\omega t - kx)\), we find:
\[ \Delta \phi = 0 \]

5. **Conclusion**:
- Therefore, the phase difference between the electric field vector E and the magnetic field vector B in an electromagnetic wave is 0.

### Final Answer:
The phase difference between the electric and magnetic field vectors E and B is **0**.

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