A plane electromagnetic wave of frequency `25 Mhz` travels in free space along the x-direction. At a particular point in space and time, `E= (6.3 j) V//m`. What is `B` at this point?

Options

A. `1.2xx10^(-6)T`
B. `1.2xx10^(-8)T`
C. `2.1xx10^(-6)T`
D. `2.1xx10^(-8)T`

Explanation

To find the magnetic field \( B \) at the given point in space and time for a plane electromagnetic wave traveling in free space, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Frequency of the wave \( f = 25 \, \text{MHz} = 25 \times 10^6 \, \text{Hz} \)
- Electric field \( E = 6.3 \, \hat{j} \, \text{V/m} \)
- Speed of light in free space \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the Relationship Between Electric and Magnetic Fields**:
- The relationship between the electric field \( E \) and the magnetic field \( B \) in an electromagnetic wave is given by:
\[ c = \frac{E}{B} \]
- Rearranging this gives:
\[ B = \frac{E}{c} \]

3. **Calculate the Magnetic Field Magnitude**:
- Substitute the values of \( E \) and \( c \):
\[ B = \frac{6.3 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]
- Performing the calculation:
\[ B = \frac{6.3}{3 \times 10^8} = 2.1 \times 10^{-8} \, \text{T} \]

4. **Determine the Direction of the Magnetic Field**:
- The electric field \( E \) is in the \( \hat{j} \) direction (y-direction).
- The wave is propagating in the \( \hat{i} \) direction (x-direction).
- According to the right-hand rule, if \( E \) is in the y-direction and the wave is propagating in the x-direction, the magnetic field \( B \) will be in the z-direction (k-direction).

5. **Express the Magnetic Field Vector**:
- Therefore, the magnetic field vector can be expressed as:
\[ B = 2.1 \times 10^{-8} \, \hat{k} \, \text{T} \]

### Final Answer:
The magnetic field \( B \) at the given point is:
\[ B = 2.1 \times 10^{-8} \, \hat{k} \, \text{T} \]